Southern  Branch 
of  the 

University  of  California 

Los  Angeles 

Porm  L.   1 

Q.C 


This  book  is  DUE  on  the  last  date  stamped  below 


MAR  1  4 


Form  L-9-15rw-8,'26 


FIRST   PRINCIPLES 


NATURAL    PHILOSOPHY 


A.  E.  DOLBEAK,  M.E.,  PH.D. 

PROFESSOR  OK  PHYSICS  AND  ASTI:I>M>MV.  TUFTS  COLLEGE,  MASS.,  AUTHOR  or 

"THE  AKT  OK  I'ROJECTI.NU,"  "TlIK  Sl'KAKINO  TELEI'HOXE," 

"MATTER,  ETHKK,  AND  MOTIOH  " 


BOSTON,  U.S.A.,  AND  LONDON 
XX    &   COMPANY,    PUBLISHERS 


1897 


COPYRIGHT,  1897 
BY    A.  E.   DOLBEAR 

ALL  RIGHTS  RESERVED 


PREFACE. 


THE  growth  of  physical  science  has  rendered  it  more 
and  more  certain  that  phenomena  of  all  kinds  and  in 
all  places  are  due  to  the  qualities  and  activities  of  the 
ultimate  atoms  of  matter. 

Astronomy,  Geology,  Chemistry,  and  Physiology  are 
each  easily  reducible  to  the  same  factors,  and  hence 
these  sciences  may  properly  be  classed  as  departments 
of  physical  science.  The  name  Physics  has  heretofore 
been  held  to  apply  to  phenomena  which  could  not  prop- 
erly be  included  in  the  above  sciences.  For  that  reason, 
and  to  emphasize  the  relationship  of  these  to  funda- 
mental physical  principles,  the  name  Natural  Philosophy 
has  been  adopted  for  this  book,  restoring  an  old  term 
to  its  proper  place,  and  giving  it  its  proper  meaning. 

The  effort  has  been  made  to  direct  the  attention  of 
the  student  from  the  physics  of  mechanism  to  the  phys- 
ics of  molecules,  and  help  him  to  carry  the  mechanical 
conceptions  gained  by  the  study  of  visible  bodies  to 
their  ultimate  particles.  The  student  is  thus  assured 
that  molecular  phenomena  can  in  this  way  be  accounted 
for  without  assuming  other  and  different  factors,  and 


iv  PREFACE. 

realizes  that  there  is  nothing  more  mysterious  in  the 
one  than  in  the  other.  Thus  the  nature  of  the  so- 
called  forms  of  energy,  and  what  it  is  that  happens  when 
energy  is  transformed,  are  made  clear  to  mechanically 
minded  persons. 

In  the  attempt  at  simplification,  some  changes  have 
been  introduced  in  the  treatment  of  energy  and  work. 
Pressure  has  been  substituted  for  force,  as  a  factor  in 
phenomena,  for  the  reason  that  if  the  latter  be  used 
in  any  other  sense  than  as  a  pressure,  it  conveys  no 
mechanical  idea.  At  best  it  is  an  indefinite  conception 
disguised  in  a  mathematical  /,  and  whatever  advan- 
tage that  may  have  for  advanced  thinkers,  it  has  none 
for  beginners. 

The  ether  has  suddenly  become  highly  important  for 
the  proper  understanding  of  the  phenomena  of  mag- 
netism, electricity,  and  light,  and  discoveries  lately 
made  have  rendered  it  needful  to  change  radically 
both  theories  and  conceptions,  and  to  restate  nearly 
the  whole  of  these  subjects.  These  changes  have  been 
incorporated  in  the  work  in  a  way  which  it  is  hoped 
will  commend  itself  to  teachers  and  be  found  easy  of 
apprehension  by  students. 

The  system  of  weights  and  measures  in  common  use 
has  been  adhered  to  throughout,  because  there  can  be  no 
confusion  of  mind  in  their  use ;  also  because  no  time 
will  need  to  be  taken  from  the  study  itself  to  learn  to 


PREFACE.  V 

think  in  and  apply  a  new  system  of  units ;  and  lastly, 
because  the  metric  system  is  used  nowhere  except  in 
laboratories,  and  not  more  than  one  in  a  thousand  of 
those  who  will  study  Natural  Philosophy  will  have 
occasion  ever  afterwards  to  use  that  system. 

No  space  has  been  given  to  the  history  of  the  science, 
but  it  is  to  be  hoped  that  every  teacher  of  the  subject 
will  add  to  the  interest  of  it  by  supplementing  the  les- 
sons with  stories  of  the  lives,  efforts,  methods,  and  suc- 
cesses of  the  men  eminent  in  all  the  fields  of  physical 
science.  Nothing  of  so  much  importance  can  take  the 
place  of  this,  but  it  should  come  from  the  teacher  rather 
than  from  an  elementary  text-book. 

A.  E.  DOLBEAR. 


CONTENTS. 


CHAPTER  I.  —  MATTER  AND  SOME  OF  ITS  PROPERTIES  : 
Physical  Science,  Matter,  Kinds  of  Matter,  Divisibility 
of  Matter,  Size  of  Molecules,  Shape  of  Atoms,  States  of 
Matter,  Porosity,  Density,  Elasticity,  Hardness,  Mass, 
Gravity 1-22 

CHAPTER   II.  —  MOTION  :  Kinds  of  Motion,  Translational, 

Vibratory,  Rotary,  Rates  of  Motion,  Acceleration     .     .      23-38 

CHAPTER   III.  —  WORK  :  Power "  39-42 

CHAPTER    IV.  — ENERGY:     Rate    of     Work,     Vibratory 

Energy,   Rotary  Energy 43-48 

CHAPTER  V.  — MACHINES:    Lever,   Pulley,   Transference 

of  Pressure  and  Power,  Transformation  of  Motion     .     .       49-55 

CHAPTER  VI.— GASEOUS  PHENOMENA:  The  Air,  Wind 
and  Gaseous  Pressure,  Air-Pump,  Barometer,  Boyle's 
Law,  Buoyancy 56-62 

CHAPTER  VII.  —  LIQUID  PRESSURE  :  Specific  Gravity,  Flo- 
tation    63-67 

CHAPTER  VIII.  —  HEAT  :  Origin  of  Heat  by  Friction,  Im- 
pact, Chemism,  Electricity,  Character  of  Heat  Motion, 
Temperature,  Thermometers,  Thermodynamics,  Heat 
Unit,  Mechanical  Equivalent,  Fuels,  Phenomena  of  Heat, 
Expansion,  Linear  and  Cubic,  Gaseous  Expansion,  Ab- 
solute Zero,  Law  of  Charles,  Specific  Heat,  Specific 
Heat  of  Gaseous  Molecules,  of  Solid  Elements,  Influence 
of  Pressure  on  Fusion,  Dissociation,  Evaporation,  Solidi- 


Vlll 


CONTENTS. 


fication,  Crystallization,  Cooling,  Surface  Tension,  Boil- 
ing Point,  Latent  Heat,  Working  Power  of  Steam,  The 
Steam-Engine,  Nature  of  Heat 68-113 

CHAPTER  IX.  —  ELECTRICITY  :  Origin  of,  In  Galvanic 
Cell,  In  Coil  and  Magnet,  In  Thermo  Pile,  Electrical  Ter- 
minology, Electrical  Measurements,  Pressure,  Action  of 
Cells,  Measure  of  the  Current,  of  Resistance,  Energy  of 
a  Battery,  Conductivity,  Magnetism,  Theory  of  Magnet- 
ism, The  Ether,  Magnetic  Field,  Induction,  Earth's  Mag- 
netism, Effect  of  Heat  on  a  Magnet,  Lifting  Power, 
Electro-Magnetism,  Electro-Magnetic  Induction,  Trans- 
former, Heating  Power  of  Current,  The  Arc  Light,  In- 
candescent Light,  The  Dynamo,  The  Motor,  The  Tele- 
graph, Chemical  Telegraph,  Mechanical  Transmitters, 
Magnetic  Telephone,  Static  Telephone,  Telegraphing 
without  Wires,  Electro-Chemical  Work,  Secondary  Bat- 
teries, High-Pressure  Phenomena,  Induction  Coils,  Geiss- 
ler's  and  Crookes'  Tubes,  Static  Electricity,  Electro- 
scope, Electric  Field,  Frictional  Electrical  Machines, 
Induction  Machines,  Leyden  Jar,  Metallic  Points,  Light- 
ning, Protection  from  Lightning,  Nature  of  Electricity  .  114-203 

CHAPTER  X.— ETHER  WAVES:  Origin  of,  Velocity  of 
Ether  Waves,  Wave-Lengths,  Number  of  Vibrations, 
Phenomena  of  Ether  Waves,  Brightness  of  Illumination, 
Action  of  Matter  upon  Ether  Waves,  Reflection,  Mul- 
tiple Reflection,  Mirrors,  Plane  and  Curved,  Images  Pro- 
duced by  Concave  Mirrors,  Refraction,  How  Light  be- 
comes Refracted,  Lenses,  Images  Formed  by  Lenses, 
Porte-Lumikre,  Projecting,  The  Lens  as  a  Magnifier, 
Compound  Microscope,  Telescope,  Spy  Glass,  Prismatic 
Refraction,  Spectrum  Analysis,  Absorption  Power  of 
Gases,  Fraunhofer  Lines,  Nebulae,  Invisible  Waves, 
Bolometer,  Photography,  Electric  Photography,  X-Ray 
Pictures,  Mechanical  Effects  of  Ether  Waves,  The  Radi- 
ometer, Double  Refraction,  Polarized  Light,  The  Nicol's 
Prism,  Interference,  Diffraction,  The  Eye  and  Vision, 
Phenomena  of  Vision,  Persistence  of,  Color  Sensation, 
Phosphorescence,  Fluorescence 204-269 


CONTENTS.  IX 


CHAPTER  XI.  —  SOUND  :  Sounding  Bodies  are  Vibrating, 
Pitch,  Energy  of  Sound,  Distributors,  Sound  Waves, 
Velocity  of  Sound,  Wave-Lengths,  Speaking  Tubes,  The 
String  Telephone,  Forced  and  Sympathetic  Vibrations, 
Resonance,  Echo,  Vibration  of  Strings,  The  Sonom- 
eter, Compound  Vibrations,  Analysis  of  Sounds,  The 
Voice,  The  Opeidoscope,  The  Phonograph,  Music,  Inter- 
ference of  Sound  Waves,  Harmony,  Change  of  Key, 
Harmonic  Interference,  The  Ear,  Limits  of  Audibility  .  270-311 

Table  of  Electrical  Resistance  of  Copper  Wires 312 

Table  of  Mechanical,  Heat,  and  Electrical  Equivalents     .     .          313 


NATUKAL   PHILOSOPHY. 

CHAPTER  I. 

MATTER    AND    SOME    OP    ITS    PROPERTIES. 

Physical  Science  has  to  do  with  the  properties  of 
matter,  its  behavior  under  all  conditions,  and  also  the 
circumstances  under  which  any  kind  of  a  change  takes 
place  in  it,  whether  it  be  one  of  place,  of  form,  or  of 
condition. 

It  is  sometimes  described  as  the  science  of  Energy, 
because  it  has  been  found  that  all  kinds  of  changes  in 
matter  are  due  to  energy  acting  in  certain  definite 
ways,  which,  when  known,  enable  one  to  foresee  what 
will  happen,  and  often  to  use  such  knowledge  for  con- 
venience, or  business,  or  pleasure. 

Every  kind  of  an  action  that  can  affect  in  any  degree 
any  of  our  senses  is  called  a  physical  action.  For 
example,  this  book  can  be  felt  by  the  sense  of  touch  ; 
it  can  be  seen  by  the  sense  of  sight ;  if  dropped  upon 
the  table,  it  can  be  heard  by  the  sense  of  hearing.  A 
peppermint  lozenge  can  be  felt,  seen,  heard,  smelled,  and 
tasted,  and  so  reach  five  of  our  senses  by  five  different 
kinds  of  physical  action.  It  can  be  felt  because  it  has 
body,  it  can  be  seen  because  light  is  reflected  from  it, 
it  can  be  heard  because  it  strikes  another  body,  it  can 


2  NATURAL   PHILOSOPHY. 

be  smelled  because  some  of  its  material  evaporates  and 
its  particles  reach  the  nerves  of  smell,  and  it  can  be 
tasted  because  some  of  its  particles  dissolve  upon  the 
nerves  of  taste  upon  the  tongue. 

Each  one  of  these  actions,  and  every  other  action 
capable  of  affecting  us  in  any  manner,  is  called  a  phenom- 
enon, so  physical  science  may  be  called  the  Science  of 
Phenomena. 

Matter.  —  Every  kind  of  an  object  that  can  affect 
our  senses  either  directly  or  indirectly  is  called  matter. 
If  the  object  be  near  at  hand  we  may  touch  it ;  if 
farther  off  we  see  it,  and  find  by  experience,  if  we 
go  to  it,  we  may  also  touch  it.  Everything  that 
shines  or  reflects  light  is  matter.  Everything  that 
has  form  or  color  or  brightness  or  taste  or  smell  or 
weight  is  properly  caMed  matter.  If  matter  be  rare, 
like  hydrogen,  to  feel  it  may  be  difficult,  but  it  may 
be  condensed  to  a  liquid,  and  then  be  sensible  to  the 
touch  and  sight. 

QUESTIONS. 

1.  Name  some  objects  and  state  which  of  the  senses  they  affect. 

2.  Describe  some  phenomenon. 

3.  Would  you  call  the  sound  of  a  bell  a  phenomenon  ? 

4.  Is  a  star  a  phenomenon  ? 

5.  Can  you  name  some  object  composed  of  matter  ? 

6.  Can  you  name  some  object  not  composed  of  matter  ? 

7.  How  does  one  become  aware  of  the  existence  of  matter? 

8.  What  reason  have  you  for  thinking  that  a  house  you  have 
never  been  near  is  composed  of  matter? 

9.  Why  do  you  infer  that  the  sun  and  moon  and  stars  are 
made  of  matter? 

10.  Can  you  think  of  some  sensation  not  due  to  matter? 


MATTER    AND    SOME   OF    ITS    PROPERTIES. 

Kinds  of  Matter.  —  By  subjecting  substances  to 
chemical  action,  such  as  dissolving  them  in  acids  or 
burning  them  in  fire,  it  has  been  found  that  most  of 
them  are  capable  of  being  broken  up  into  two  or 
more  constituents,  thus  showing  them  to  be  compound 
bodies.  This  is  the  case  with  wood,  stones,  earth, 
water,  etc.  These  ultimate  constituent  parts  are  called 
Elements. 

About  seventy  different  elements  are  now  known. 
Some  of  them  all  persons  are  familiar  with,  such 
as  gold,  silver,  nickel,  copper,  iron,  lead,  tin,  zinc, 
carbon.  Other  elements  less  familiar  are  antimony, 
silicon,  calcium,  bismuth,  aluminum,  oxygen,  hydrogen, 
nitrogen  ;  some  are  exceedingly  rare,  such  as  didymium, 
gallium,  lanthanum.  Each  of  these  elements  differs 
from  every  other  in  its  physical  and  chemical  prop- 
erties, so  it  may  be  identified  and  separated  from  every 
combination  containing  it.  Gold  is  yellow,  copper  red, 
and  silver  white.  Some  enter  into  chemical  combination 
very  easily,  such  as  iron  and  oxygen,  forming  a  mineral 
that  is  so  plentiful  as  to  form  great  hills  and  beds  ; 
it  is  called  iron  ore.  O  the  re  will  not  enter  into 
combination  under  ordinary  conditions.  For  instance, 
carbon  may  be  kept  for  an  indefinite  time  exposed 
to  air,  water,  or  acids,  and  not  be  affected  by  them. 
There  is  good  reason  for  thinking  that  most  of  the 
body  of  the  earth  is  composed  of  iron ;  but  the  rocks 
that  make  up  most  of  the  land  surface  are  com- 
posed of  aluminum,  oxygen,  silicon,  calcium,  and  car- 
Ion,  while  the  water  is  a  compound  of  oxygen  and 
hydrogen. 


NATURAL   PHILOSOPHY. 


QUESTIONS. 

1.  Name  some  of  the  common  kinds  of  matter  you  chance  to 
be  familiar  with. 

2.  Do  you  know  whether  they  are  elements  or  compounds  ? 

3.  How  many  of  the  elements  have  you  ever  seen  ? 

4.  How  do  those  you  have  seen  differ  from  each  other  V 

5.  How  could  you  find  out  the  composition  of  a  substance  ? 

6.  How  would  you  know  lead  from  tin  ? 

Divisibility  of  Matter.  —  A  lump  of  salt  may  be 
pounded  into  dust  so  fine  that  a  particle  could  be  seen 
only  by  looking  through  a  microscope,  which  might 
show  it  to  be  no  bigger  than  the  hundred-thousandth 
of  an  inch ;  but  if  the  lump  of  salt  be  put  into  water 
the  smallest  particle  produced  by  pounding  will  be  dis- 
solved into  more  minute  parts.  Yet  this  process  cannot 
go  on  without  limit.  There  is  a  smallest  part  of  salt, 
which,  if  broken  up  into  pieces,  is  no  longer  salt,  but 
the  elements  which  were  united  to  form  the  salt,  — 
namely  sodium  and  chlorine.  The  smallest  part  into 
which  any  substance  may  be  divided  without  destroying 
its  qualities  is  called  a  molecule,  while  the  constituents 
of  the  molecule  are  called  atoms.  Thus  a  molecule  of 
salt  is  composed  of  an  atom  of  sodium  combined  with 
an  atom  of  chlorine,  and  is  chemically  written  NaCl. 
A  molecule  of  water  is  composed  of  two  atoms  of 
hydrogen  and  one  atom  of  oxygen,  and  is  written  H2O. 
Chemistry  is  the  science  that  treats  of  the  combi- 
nation of  atoms  into  molecules,  and  the  proper  con- 
ditions for  combining  or  separating  substances  in  order 
to  produce  any  desired  kind  of  matter,  either  simple  or 


MATTER    AND    SOME   OF    ITS    PROPERTIES. 


LIST   OF  COMMON  ELEMENTS   AND   THEIR 
CHEMICAL   SYMBOLS. 


NAME  OF  ELEMENT. 

SYMBOL. 

AT.WT. 

IMINSII  V. 

HARDNESS. 

MELT.  POINT. 

Aluminum 

Al 

27 

2.6 

3 

1260 

Antimony 

Sb 

120 

6.7 

3 

790 

Arsenic 

As 

75 

5.7 

3 



Bismuth 

Bi 

208 

9.8 

2 

522 

Bromine 

Br 

80 

3.1 

— 

20 

Calcium 

Ca 

40 

1.6 

1 

1200 

Carbon 

C 

12 

2 

1.10 



Chlorine 

Cl 

35.5 

1.3 





Copper 

Cu 

63.2 

8.9 

3 

1900 

Gold 

Au 

196 

19.3 

3 

1900 

Hydrogen 

II 

1 

— 

— 

— 

Iodine 

I 

126 

5 



230 

Iron 

Fe 

56 

7.8 

5 

2900 

Lead 

Pb 

207 

11.3 

2 

600 

Magnesium 

Mg 

24 

1.7 

o 

1170 

Mercury 

Hg 

200 

13.6 

— 

— 

Nickel 

Xi 

58 

8.9 

4 

2700 

Nitrogen 

N 

14 

,  — 

— 

— 

Oxygen 

b 

16 

— 

— 

— 

Phosphorus 

p 

31 

1.8 

— 

110 

Platinum 

pt 

195 

21.5 

4 

3400 

Potassium 

K 

39 

.87 



140 

Silicon 

Si 

28 

2.3 

— 



Silver 

Ag 

108 

10.5 

2 

1800 

Sodium 

Xa 

23 

.98 



200 

Sulphur 

S 

32 

2 

2 

235 

Tin 

Sn 

118 

7.2 

o 

440 

Zinc 

Zn 

65 

7 

3 

780 

6  NATURAL  PHILOSOPHY. 

compound.  Under  ordinary  conditions  of  temperature 
most,  if  not  all,  of  the  elementary  atoms  combine  with 
their  like  if  there  be  no  other  kind  present  with  which 
they  can  unite  :  hydrogen  unites  with  hydrogen,  one 
atom  of  each,  H,H  ;  oxygen,  O,O ;  carbon,  C,C ;  and 
so  on ;  and  special  means  have  to  be  applied  to  obtain 
matter  in  its  atomic  form.  Hence  iron,  carbon,  oxygen, 
sulphur,  are  molecular  in  constitution,  but  of  similar 
atoms,  while  compound  substances  are  molecular  but  of 
dissimilar  atoms. 

Some  molecules  consist  of  but  two  or  three  atoms,  as 
NaCl,  H2O,  while  others  may  have  tens  and  hundreds 
of  atoms.  For  example,  a  molecule  of  albumen  from 
the  white  of  an  egg  consists  of  C210H330N52O66S3,  661 
atoms.  It  must  be  evident  that  molecules  vary  much 
in  size.  Gold  may  be  beaten  out  into  leaves  less  than 
the  millionth  of  an  inch  thick;  and  it  must  be  more 
than  one  molecule  thick,  or  it  could  not  hold  together. 
The  tiniest  bit  of  silver  dissolved  in  nitric  acid  will 
render  milky  a  hundred  cubic  inches  of  a  solution  of 
common  salt.  If  the  silver  be  the  .001  of  an  inch 
cube,  it  wiU  have  been,  divided  into  10003  X  100  = 
100000,000000  parts. 

Drop  a  bit  of  aniline  the  size  of  a  pin's  head  into  a 
quart  of  water.  It  will  give  decided  color  to  it.  Cal- 
culate how  many  times  the  volume  of  water  is  greater 
than  that  of  the  aniline,  to  find  how  many  parts  the 
latter  has  been  divided  into.  Half  fill  a  test  tube  with 
the  colored  liquid  and  fill  up  with  water;  this  will 
dilute  it  one-half  and  double  the  number  of  divisions. 
This  may  be  continued  until  the  color  ceases  to  be 


MATTER    AND    SOME    OF    ITS    PROPERTIES.  7 

discernible.  Still  finer  divisions  may  be  perceived  by 
dissolving  in  a  similar  way  eosiri  and  resorcin. 

Size  of  Molecules. —  Blow  a  soap-bubble  and  observe 
the  bands  of  color  that  flow  down  the  sides.  After  the 
last  purplish  tint  comes  a  white  band  ;  and  following 
this  is  a  dark  gray  patch  from  which  but  little  light  is 
reflected.  The  thickness  of  this  gray  patch  has  been 
shown  to  be  but  the  Tl¥  of  the  wave-length  of  the 
purple  light,  which  is  in  the  neighborhood  of  g^^  of 

an  inch,  g ^oo  X  T^  =  -i^fonnF'  hence  the  thick' 
ness  of  the  film  of  the  bubble  cannot  be  far  from  one 
ten-millionth  of  an  inch.  Yet  it  possesses  tensile 
strength  enough  to  hold  up  the  weight  of  the  bubble, 
and  therefore  is  greater  probably  than  one  molecule 
thick ;  if  it  be  two  molecules  thick  their  diameters  will 
be  but  one  twenty-millionth  of  an  inch,  and  if  the  film 
be  five  molecules  thick,  each  must  be  about  the  fifty- 
millionth  of  an  inch  in  diameter.  Various  phenomena 
indicate  that  the  size  of  molecules  of  two  or  three 
atoms  is  from  the  fifty-millionth  to  the  hundred- 
millionth  of  an  inch,  the  atoms  being  correspondingly 
smaller.  For  most  purposes  it  will  be  convenient  to 
bear  in  mind  that  about  fifty  million  molecules  in  a 
row  would  reach  an  inch,  and  the  number  in  a  cubic 
inch,  say  of  water  or  iron,  would  be  the  cube .  of  fifty 
millions,  125000,000000,000000,000000.  (Where  such 
large  numbers  occur  it  is  customary  to  write  the 
significant  figures  multiplied  by  ten  raised  to  the 
power  indicated  by  the  number  of  ciphers.  Thus  the 
above  would  be  125  X  1021.$ 


8  NATURAL   PHILOSOPHY. 

Molecules  with  a  large  number  of  atoms  must  of 
course  be  correspondingly  larger,  so  that  the  diameter 
of  a  molecule  of  albumen,  containing  over  600  atoms, 
would  probably  be  eight  or  nine  times  that  of  water, 
that  is,  about  the  millionth  of  an  inch.  As  the  highest 
power  of  the  microscope  enables  one  to  see  a  particle 
but  about  the  hundred-thousandth  of  an  inch  in  dia- 
meter, it  is  clear  it  could  not  make  visible  a  molecule 
even  of  the  largest  size,  and  the  smallest  particle 
visible  would  contain  not  less  than  a  hundred  million 
atoms.  If  one  would  gain  something  of  an  idea  what 
a  prodigious  number  of  atoms  there  are  in  a  cubic  inch 
of  ordinary  matter,  let  him  compute  how  long  a  time  it 
would  take  to  count  them  at  any  definite  rate,  say  one 
thousand  or  a  million  a  second. 

QUESTIONS. 

1.  What  reason  is  there  for  thinking  that  there  is  a  limit  to 
the  divisibility  of  matter  ? 

2.  What  is  the  difference  between  the  sciences  of  physics  and 
chemistry  ? 

3.  What  is  the  distinction  between  an  atom  and  a  molecule  ? 

4.  Are  the  elements  ordinarily  found  in  the  atomic  or  in  the 
molecular  state  ? 

5.  How  many  atoms  are  there  in  a  molecule  ? 

6.  Can  you  find  in  any  book  on  chemistry  a  molecule  with 
more  atoms  than  there  are  in  albumen  ? 

7.  How  many  molecules  of  albumen  will  there  be  in  a  cubic 
inch  if  each  atom  in  the  molecule  be  the  fifty-millionth  of  an  inch 
in  diameter  ? 

8.  If  a  grain  of  aniline  will  give  color  to  a  cubic  foot  of  water 
weighing  62£  pounds,  into  how  many  parts  has  the  aniline  been 
divided  ? 


MATTER    AND    SOME    OF    ITS    PROPERTIES.  9 

9.  Can  you  think  of  any  reason  why  that  number  does  not 
represent  the  limit  of  division  of  the  aniline  ? 

Shape  of  Atoms.  —  It  was  formerly  thought  that 
atoms  must  be  minute  solid  spherical  particles,  so  hard 
they  could  not  wear  out,  but  now  it  is  believed  that 
such  kinds  of  atoms  could  not  possibly  present  such 
phenomena  as  matter  actually  pos- 
sesses, and  there  is  an  increasing 
probability  that  atoms  are  minute 
vortex  rings,  similar  in  form  to  such 
rings  as  are  sometimes  puffed  out 
from  a  locomotive  in  still  air,  where 
they  may  be  seen  to  rise  a  hundred 
or  more  feet  high,  vibrating  and 
wriggling  in  a  curious  way,  but  maintaining  their  ring 
form  until  dissolved  in  the  air.  Such  rings1  possess 
form,  rigidity,  elasticity,  inertia,  and  energy.  If  it 
were  not  for  the  friction  in  the  air,  when  once  formed 

1  Vortex  rings  for  illustration  may  be  made  by  having  a  wooden  box  about  a 
foot  on  a  side,  with  a  round  orifice  in  the  middle  of  one  side,  and  the  side  opposite 
covered  with  stout  cloth  tightly  stretched  over  a  framework.  A  saucer  containing 


strong  ammonia  water,  and  another  containing  strong  hydrochloric  acid,  will 
cause  dense  fumes  in  the  box,  and  a  tap  with  the  hand  upon  the  cloth  back  will 
force  out  a  ring  from  the  orifice.  These  may  be  made  to  follow  and  strike  each 


10  NATURAL   PHILOSOPHY. 

they  would  be  practically  indestructible  things,  possess- 
ing on  a  large  scale  such  properties  as  atoms  exhibit  on 
a  minute  scale.  Atomic  vortex  rings  are  supposed  to  be 
constituted  of  ether,1  which  is  known  to  be  frictionless. 
There  is  now  no  other  theory  of  atoms  than  this  one, 
and  'it  does  not  appear  that  there  are  any  serious 
objections  to  it.  For  that  reason  such  atoms  will  be 
assumed  throughout  this  book. 

QUESTIONS. 

1.  Take  up  a  small  drop   of  water  on  the  point  of  a  pin. 
Estimate  its  size,  and  compute  how  many  molecules  of  water 
make  it  up. 

2.  AJalood-corpuscle  is  about  the  three-thousandth  of  an  inch 
in  diameter  and  one-fifth  as  thick;    how  many  such  can  there 
be  in  a  cubic  inch  of  blood? 

3.  How  many  molecules  are  there  in  a  cubic  inch  of  air  if  they 
are  two-hundred-thousandth  of  an  inch  apart  on  the  average  ? 

4.  If  the  space  of  a  cubic  inch  were  made  a  perfect  vacuum, 
and  a  minute  hole  made  into  it,  and  ten  million  molecules  of  air 
a  second  were  to  go  through,  how  long  would  it  take  to  be  filled  ? 

States  of  Matter.  —  As  the  atoms  and  molecules  are 
much  too  small  to  be  seen,  what  we  do  see  is  made  up 
of  immense  numbers  of  them  compacted  together.  If 
the  molecules  cohere  so  strongly  in  fixed  positions 
that  they  do  not  fall  apart  easily  we  call  the  body  a 
solid  body.  A  book  or  pencil  or  stone  is  an  example 
of  a  solid ;  and  there  are  all  degrees  of  compact- 
other,  rebounding  and  vibrating,  apparently  attracting  each  other  and  being 
attracted  by  neighboring  bodies. 

By  filling  the  mouth  with  smoke  and  pursing  the  lips  as  if  to  make  the  sound 
O  one  may  make  fifteen  or  twenty  small  rings  by  snapping  the  cheek  with  the 
finger.  '  See  page  138. 


MATTER    AND    SOME   OF   ITS    PROPERTIES.  11 

ness  or  solidity.  When  molecules  have  but  slight 
attraction  for  each  other,  and  may  be  separated  very 
easily,  the  body  is  called  a  liquid.  The  molecules  of 
water  cohere  slightly,  else  they  would  not  be  formed 
into  a  drop.  When  water  is  poured  into  a  pitcher  or 
other  vessel  it  immediately  assumes  the  shape  of  the 
containing  vessel ;  for  a  liquid  has  no  particular  form, 
except  that  a  small  quantity,  like  a  drop,  will  assume  a 
spherical  form  if  free  in  the  air,  and  a  spheroidal  form 
when  resting  upon  a  surface  it  cannot  wet.  Drop 
gently  a  little  water  upon  a  painted  or  varnished 
surface  and  notice  the  rounded  edges  and  flattened  top 
it  assumes.  The  smaller  the  drop  the  more  nearly  it  is 
spherical.  The  same  may  lie  seen  still  better  by  using 
a  little  mercury  instead  of  water.  This  shows  slight 
molecular  attraction.  Indeed  it  appears  as  if  the  mole- 
cules can  move  freely  among  themselves,  and  do  not 
cohere  in  any  fixed  positions. 

The  molecules  of  some  substances  do  not  cohere  at 
all,  but  act  as  if  each  one  endeavored  to  get  as  far  from 
the  rest  as  it  could  ;  and  being  free  to  move  each  bumps 
against  its  neighbors  and  rebounds  from  them,  so  that  a 
quantity  of  such  free  roving  molecules  has  no  particular 
shape  under  any  conditions,  but  practically  fills  all  the 
space  of  any  vessel  in  which  it  may  be  inclosed,  as  a 
swarm  of  flies  might  do.  Such  free  roving  molecules 
without  cohesion  is  called  a  gas,  and  a  single  one  is  called 
a  gaseous  molecule.  The  air  we  breathe  is  an  example. 
If  a  bottle  of  ammonia  water  be  opened,  the  ammonia 
gas  will  escape,  and  presently  may  be  detected  through- 
out the  room.  Odors  of  all  sorts  are  gases,  whose  indi- 


12  NATURAL   PHILOSOPHY. 

vidual  molecules  are  free  to  move  in  every  direction. 
One  may  imagine  a  single  molecule  of  any  kind  in  a 
room.  Now  it  may  be  here  and  now  there.  It  would 
not  be  possible  to  detect  a  single  one,  but  when  numer- 
ous enough  some  may  be  detected  by  smell,  as  cologne ; 
some  by  chemical  methods.  Remove  the  stoppers  from 
a  bottle  of  hydrochloric  acid  and  one  of  ammonia  when 
they  stand  a  foot  or  two  apart,  and  a  white  cloud  will  be 
formed  in  the  air  between  them.  If  any  gases  are  con- 
densed so  as  to  bring  their  molecules  into  approximate 
contact  and  held  there,  they  form  a  liquid.  Such 
condensation  of  gases  may  be  effected  by  cold  and 
pressure ;  and  so  ammonia,  air,  oxygen,  and  indeed  all 
gases  have  been  reduced  to  liquids,  and  some  even  to 
the  solid  form,  as  in  the  case  of  carbonic  acid  gas. 
A  solid  will  maintain  its  shape  and  volume.  A  liquid 
assumes  the  shape  of  the  containing  vessel  while  its 
volume  remains  the  same ;  but  a  gas  keeps  neither 
shape  nor  volume,  except  when  confined. 

These  three  states  of  matter  depend  almost  altogether 
upon  temperature.  For  instance  below  32°  the  liquid 
water  becomes  ice,  a  solid,  and  above  212°  it  becomes 
steam,  a  gas.  Below  — 39°  mercury  becomes  a  solid, 
and  at  357°  it  is  a  gas.  Iron,  platinum,  and  all  the 
solid  metals  are  converted  into  gases  by  the  heat  of  an 
electric  arc ;  while  earth,  stones,  and  such  solids  are 
either  fused  to  liquids,  like  the  lava  of  volcanoes,  or 
are.  vaporized,  which  is  but  another  name  for  assuming 
the  gaseous  form.  At  the  sun  it  is  probably  so  hot  that 
there  are  no  solids.  At  the  moon  it  is  probably  so  cold 
that  there  are  no  liquids  or  gases. 


MATTER    AND    SOME    OF    ITS    PROPERTIES.  13 

At  the  earth's  surface  the  air  particles  have  a  free 
path  to  move  in,  between  collisions,  over  two  hundred 
times  their  diameter.  If  a  molecule  were  magnified  to 
the  size  of  a  honey-bee,  then  the  corresponding  space  for 
free  movement  would  be  about  ten  feet  without  coming 
in  contact  with  another  molecule.  As  one  ascends 
above  the  surface  of  the  earth  the  air  is  less  and  less 
dense,  —  that  is,  there  is  a  smaller  number  of  molecules 
to  the  cubic  inch,  and  each  molecule  has  more  and 
more  free  space  to  move  in,  a  longer  free  path.  At  the 
height  of  200  miles  a  molecule  might  have  a  free  path 
of  50,000,000  miles  without  colliding  with  another. 

Porosity.  —  As  there  is  so  great  a  distance  between 
the  molecules  of  common  air,  it  is  plain  that  there  is 
room  for  others  of  any  kind  that  may  chance  to  be 
present.  Indeed,  that  molecules  of  ammonia  or  other 
gas  become  diffused  through  the  air  is  evidence  that 
the  air  particles  do  not  occupy  all  the  space.  But  a 
liquid  differs  from  a  gas  in  having  its  molecules  closer 
together ;  but  even  then  they  do  not  occupy  all  the 
space.  Salt,  sugar,  and  many  other  things  will  dissolve 
in  water  without  increasing  its  bulk  appreciably,  which 
shows  that  there  are  spaces  between  water  molecules 
where  other  molecules  may  find  place.  The  same  is 
true  of  solids.  Gold  and  silver  will  dissolve  in  mn- 
cury  nearly  as  freely  as  salt  in  water,  and  a  drop  of 
mercury  will  be  absorbed  by  most  metals  like  water 
into  wood.  This  fact,  that  solids  and  liquids  are  able 
to  share  their  space  with  other  substances,  is  called 
porosity,  and  is  due  to  the  fact  that  the  molecules  of 


14  NATURAL   PHILOSOPHY. 

all  substances,  even  the  densest,  are  not  in  such  contact 
as  to  take  up  all  the  space.  If  the  molecules  were 
shaped  like  marbles  there  would  be  inter-molecular 
spaces.  Fill  a  cup  with  marbles  or  shot  and  a  good 
deal  of  water  can  then  be  poured  into  the  cup.  When 
it  is  apparently  filled  with  water,  a  good  deal  of  sugar 
can  be  added.  If  the  atoms  are  ring-shaped,  they  must 
still  leave  a  good  deal  of  unoccupied  space.  Water  can 
be  squeezed  through  iron  an  inch  thick,  and  gases 
through  gold  and  platinum.  The  pressure  of  the  wind 
is  quite  sufficient  to  force  air  in  a  steady  stream 
through  brick  and  plastered  walls  a  foot  thick. 

QUESTIONS. 

1.  How  do  solids  differ  from  liquids  ? 

2.  Whittle  small  flat  surfaces  on  two  bits  of  lead,  and  press 
the  surfaces  together  with  a  slight  twisting  movement.     Note 
what  happens,  and  describe  it. 

3.  Can  you  do  the  same  for  wood?     If  not,  why  not  ? 

4.  How  does  it  happen  that  gaseous  molecules  fill  any  kind  of 
a  vessel  they  chance  to  be  in  ? 

5.  Is  it  true  for  all  quantities  of  gas  ?     Why  ? 

6.  What  idea  have  you  of  a  gas  and  why  it  behaves  as  it  does  ? 

7.  What  causes  the  difference  between  ice,  water,  and  steam  ? 

8.  Can  you  imagine  how  it  does  it  ? 

9.  Name  substances  you  know  to  be  porous.     How  do  you 
know  them  to  be  so  ? 

10.  What  reason  is  there  for  thinking  that  water  is  porous  ? 

11.  If  matter  filled  space  would  it  be  porous  ? 

Density.  —  By  this  is  meant  the  amount  of  matter 
in  a  given  space.  If  two  cubic  inches  of  air  are  made 
to  occupy  the  space  of  one  cubic  inch,  then  there  is 


MATTER    AND   SOME   OF    ITS    PROPERTIES.  15 

twice  as  much  air  in  that  space  as  before,  and  we  say 
the  density  is  twice  as  great.  The  number  of  mole- 
cules per  cubic  inch  determines  the  density,  but  it 
would  be  inconvenient  to  employ  such  a  number  if  it 
could  be  accurately  found.  We  use  instead  the  weight 
of  bodies  to  determine  their  density.  Water  is  taken 
as  a  standard  for  solids  and  liquids.  A  cubic  foot  of 
water  weighs  62£  pounds.  If  a  cubic  foot  of  iron 
weighs  468  pounds,  we  say  that  the  density  of  iron 

is  7.5,  for  HI  =  7.5. 

In  the  Table  of  Elements  on  page  5  is  a  column 
giving  the  relative  densities  of  the  elements.  The 
numbers  signify  how  many  times  heavier  the  substance 
is  than  an  equal  volume  of  water.  Thus,  the  density 
of  aluminum  is  2.6  ;  gold,  19.3.  The  numbers  also 
represent  the  specific  gravity  of  the  different  elements  ; 
and  how  they  may  be  determined  is  shown  on  page  65. 

For  gases,  either  hydrogen  or  common  air  is  used  as 
a  standard :  100  cubic  inches  of  air  weigh  31  grains. 
[When  hydrogen  is  employed,  the  standard  volume  is  a 
liter  (1000  cubic  centimeters),  which,  at  standard  tem- 
perature (32°)  and  pressure  (30  inches  of  mercury), 
weighs  0.0896  of  a  gram.] 

QUESTIONS. 

1.  A  cubic   foot  of  marble  weighs  168  pounds;  what  is  its 
density  ? 

2.  If  the  density  of  lead  be  11.3,  how  much  will  a  cubic  foot 
weigh  ? 

:'>.  What  must  a  bar  of  iron  weigh  that  is  an  inch  square  and 
a  foot  long  ? 


16  NATURAL   PHILOSOPHY. 

4.  How  much  does  a  cubic  foot  of  air  weigh  ? 

5.  What  volume  of  air  weighs  100  pounds  ? 

6.  How  much  does  a  cubic  foot  of  gold  weigh  ? 

7.  If  a  gallon  of  alcohol  weighs  50  pounds,  what  is  its  density? 

8.  If  the  density  of  the  earth  be  5.6,  how  many  tons  does  it 
weigh? 

Elasticity.  —  When  a  piece  of  India  rubber  is 
stretched  and  then  released  it  returns  to  its  original 
length.  Likewise  a  rubber  ball,  if  pinched,  will  be 
deformed,  but  it  will  regain  its  spherical  shape  as  soon 
as  the  pressure  is  removed.  This  ability  of  a  body  to 
recover  its  original  form  after  distortion  is  called  elas- 
ticity, and  all  bodies  possess  it  in  some  degree,  but  with 
great  differences.  Glass,  ivory,  and  tempered  steel  are 
highly  elastic.  Putty,  dough,  and  wet  clay  have  but  a 
slight  degree  of  this  property.  All  liquids  are  very 


elastic.  Water,  if  compressed,  as  it  may  be,  will 
recover  its  original  volume  at  once,  no  matter  how  long 
a  time  it  has  been  kept  under  stress.  Gases  also 
possess  elasticity,  which  depends  upon  their  tempera- 
ture, and  there  is  reason  for  thinking  that  the  ultimate 


MATTER   AND    SOME    OF    ITS    PROPERTIES.  17 

atoms  have  this  property  as  one  of  their  essential  ones. 
When  vortex-rings  collide^they  bound  away  from  each 
other  as  billiard  balls  will  do ;  and  they  may  be  seen  to 
vibrate,  their  sides  swinging  to  and  fro  like  the  prongs 
of  a  tuning-fork  that  has  been  struck  (Fig.  3) ;  and  for 
a  similar  reason  they  endeavor  to  recover  their  original 
form. 

A  ring  made  of  steel  or  brass  wire  6  or  8  inches  in 
diameter,  if  pulled  out  to  an  ellipse  with  thumb  and 


fingers  and  then  let  go,  will  vibrate  well,  and  show  this 
elasticity  due  to  form. 

Hardness.  —  A  piece  of  pine  wood  can  be  cut  easier 
than  a  piece  of  oak,  and  a  piece  of  oak  easier  than  a 
piece  of  brass,  and  brass  easier  than  steel.  There  are 
all  degrees  of  difficulty  of  this  kind  in  substances  of 
different  sorts.  We  say  one  substance  is  harder  than 
another  when  it  is  less  easily  cut  or  scratched ;  but  when 
one  cuts  any  substance  he  is  separating  the  molecules 
of  that  substance  and  these  cohere  with  different 
degrees  of  strength.  The  same  attraction  that  causes 
atoms  to  combine  into  molecules  causes  molecules  to 
adhere  together.  Only  for  convenience  we  speak  of 
the  former  as  chemical  attraction  or  chemism,  while  the 
latter  is  called  cohesion  or  adhesion  ;  and  the  hardness 
of  a  body  depends  on  how  strongly  the  adjacent  mole- 


18  NATURAL   PHILOSOPHY. 

cules  stick  together.  The  terms  hard  and  soft  do  not 
apply  to  gases  or  liquids,  because  their  molecules  have 
little  or  no  attraction  for  each  other ;  only  solids 
exhibit  it,  and  its  chief  importance  is  as  characteristic 
of  minerals.  A  scale  of  hardness  has  been  devised 
from  talc,  which  is  the  softest  of  minerals,  and  may  be 
cut  without  dulling  a  knife  much,  to  the  diamond, 
which  is  the  hardest  of  known  bodies. 

SCALE   OF   HARDNESS. 

1.  Talc.  6.  Feldspar. 

2.  Gypsum.  7.  Quartz. 

3.  Calcspar.  8.  Topaz. 

4.  Fluorspar.  9.  Sapphire. 

5.  Apatite.  10.  Diamond. 

Each  one  of  these  in  their  order  will  scratch  the  one 
preceding  it,  and  will  not  be  scratched  by  it.  Quartz 
will  scratch  feldspar,  and  the  diamond  will  scratch 
sapphire  ;  but  only  diamond-dust  will  scratch  the 
diamond.  But  even  among  diamonds  there  is  as  great 
a  variety  in  hardness  as  there  is  among  other  minerals. 
Some  are  so  hard  they  cannot  be  scratched  at  all,  and 
cannot  be  used  as  gems  because  they  cannot  be  properly 
shaped.  A  body  may  be  hard  yet  fragile,  for  a  blow 
with  a  hammer  that  would  not  affect  a  piece  of  steel 
with  a  hardness  of  7  would  break  a  diamond  into  many 
fragments.  Some  of  the  metallic  elements  are  so  soft 
they  may  be  moulded  into  any  form  in  the  fingers. 
Such  is  the  case  with  sodium  and  potassium ;  also 
with  selenium  at  a  temperature  of  140°  F. 


MATTER    AND    SOME    OF    ITS    PROPERTIES.  19 

In  the  Table  of  Elements  (page  5)  is  given  a  column 
containing  the  hardness  of  such  as  are  solid. 

Mass.  —  We  determine  the  amount  of  matter  in  a 
given  substance  by  weighing  it.  There  is  twice  as 
much  matter  in  two  pounds  of  sugar  or  of  iron  as  there 
is  in  one  pound;  and  there  is,  therefore,  as  much 
matter  in  a  pound  of  sugar  as  there  is  in  the  pound- 
weight  that  balances  it  on  the  scales.  The  amount  of 
matter  in  a  body,  as  determined  by  properly  weighing 
it,  and  independent  of  its  volume,  is  called  its  mass. 
A  pound  of  feathers  may  occupy  a  cubic  foot,  or  it  may 
be  condensed  to  a  few  cubic  inches.  In  either  case  the 
number  of  molecules  is  the  same,  the  weight  the  same, 
and  therefore  the  mass  is  independent  of  the  space  the 
matter  occupies.  But  the  weight  of  a  body  is  caused 
by  the  attraction  of  the  earth,  and  such  attraction  varies 
with  the  distance  from  the  surface  of  the  earth.  At  the 
center  of  the  earth  a  body  would  weigh  nothing,  because 
equally  attracted  on  all  sides,  and  therefore  would  not 
tend  to  move  in  any  direction.  At  the  distance  of 
10,000  miles  from  the  earth,  the  attraction  of  the  earth 
would  be  small  upon  it,  and  it  would  consequently 
have  small  weight.  In  either  case  the  number  of  mole- 
cules would  be  the  same,  and  the  mass  would  be  the 
same.  There  is  another  way  of  determining  mass, 
without  weighing,  described  on  page  21.  Atoms  of  the 
different  elements  have  different  masses.  They  are 
represented  in  the  Table  of  Elements,  page  5,  by  the 
numbers  in  the  column  marked  "atomic  weight,"  in 
which  the  mass  of  an  atom  of  hydrogen  is  called  unity. 


20  NATURAL   PHILOSOPHY. 

Thus,  the  atom  of  oxygen  has  16  times  the  mass  of 
hydrogen  ;  that  is,  it  takes  16  atoms  of  hydrogen  to 
weigh  as  much  as  one  of  oxygen.  An  iron  atom  has 
56  times,  and  a  gold  atom  196  times  the  mass  of  a 
hydrogen  atom. 

Gravity.  —  That-  the  earth  attracts  bodies  so  as  to 
give  to  them  weight  has  been  known  for  hundreds  of 
years.  Newton  discovered  that  all  matter  was  thus 
attractive  ;  that  every  atom  of  matter  attracts  every 
other  atom  in  the  universe,  the  strength  of  the  attrac- 
tion between  two  bodies  depending  upon  the  quantity 
or  mass  of  matter  and  the  distance  between  them. 
The  law  of  gravitation  is,  every  atom  of  matter  attracts 
eveiy  other  atom.  The  strength  of  the  attraction 
varies  with  the  mass  of  each  atom,  and  is  inversely  as 
the  square  of  their  distance  apart,  that  is,  the  attrac- 
tion of  two  atoms  of  a  given  kind  for  another  atom  is 
twice  as  much  as  the  attraction  of  one  ;  and  when  the 
distance  between  two  masses  is  doubled,  their  attraction 
is  reduced  to  one-fourth.  If  the  distance  be  tripled, 
their  mutual  pull  upon  each  other  will  be  only  one- 
ninth,  and  so  on.  Gravitative  attraction  is  very  weak 
between  masses  of  only  a  few  pounds,  and  requires 
very  delicate  experiments  to  enable  one  to  observe  it. 
When  one  considers  the  enormous  number  of  atoms 
that  compose  the  earth,  the  moon,  and  the  sun,  he  will 
see  that  the  weak  attraction  of  a  one-pound  mass  is 
multiplied  by  thousands  of  millions.  The  attraction 
between  the  earth  and  the  moon  is  equal  to  twenty 
quadrillion  tons. 


MATTER    AND    SOME    OF    ITS    PROPERTIES.  21 

The  strength  of  the  earth's  gravitative  attraction  is 
measured  from  its  center,  which  is  4000  miles  from  its 
surface  ;  hence,  a  mass  that  weighs  one  pound  at  the 
surface  of  the  earth  would  weigh  but  one-fourth  of  a 
pound  4000  miles  above  the  earth,  for  the  distance 
from  the  center  is  doubled,  and  at  the  distance  of  the 
moon,  240,000  miles  (60  X  4000),  only  the  thirty-six- 

hundredth  of  a  pound  (  — ^  j .     At  the  surface  of  the 

sun  the  strength  of  gravitative  attraction  is  28  times  its 
value  upon  the  earth,  so  that  a  person  weighing  150 
pounds  here  would  weigh  there  150  X  28  =  4200 
pounds,  nearly  two  tons,  and  of  course  would  be  quite 
unable  to  move.  The  sun  attracts  every  ton  on  the 
earth  with  a  pull  of  a  little  more  than  a  pound.  An 
equal  mass  upon  the  moon  is  attracted,  by  the  earth 
with  a  pull  of  10  ounces. 

As  the  weight  of  a  body  depends  upon  the  attraction 
of  gravitation  at  the  place  where  it  chances  to  be,  if 
the  weight  of  the  body  be  divided  by  the  value  of 
gravity,  the  quotient  will  be  the  same  quantity  at  all 
times  and  all  places.  Thus,  if  the  value  of  gravity  orT 
the  earth  be  32,  and  at  the  sun  28  X  32  =  896,  a 
body  weighing  one  pound  on  the  earth  would  be 
represented  by  ^ .  On  the  sun  the  same  body  would 

1  X  28         1 

weigh  28,  and  would  be  represented  by  —          =  — , 

oyb          oZ 

precisely  the  same  quantity. 

Let  w  equal  the  weight  of  a  body,  and  g  the  value 

of  gravity  where  the  body  may  be,  then  —  =  a  constant 


22  NATURAL   PHILOSOPHY. 

quantity ;    and  this  is  sometimes  treated  as  the  mass 
of  the  body.     If  m  —  the  mass,  then  one  may  write, 

—  =  m.      The    fraction   ^ ,  as    above,    is   sometimes 

tJ 

called  a  poundal. 

QUESTIONS. 

1.  If  a  ton  were  raised  4000  miles  above  the  surface  of  the 
earth,  what  would  it  weigh  there  ? 

2.  Would  its  mass  be  any  less  ? 

3.  Do  you  think  you  could  move  it  by  pushing  any  easier  than 
at  the  earth's  surface  ?. 

4.  How  far  away  must  it  be  removed  in  order  to  weigh  one 
pound? 

5.  What  is  the  difference  between  weight  and  mass? 

6.  How  far  from  the  earth  must  a  body  be  moved  that  it 
shall  weigh  nothing? 

7.  Would  it.  make  any  difference  in  which  direction  a  body 
should  be  moved  ? 

8.  Would  you  think  there  might  be  a  point  between  the  moon 
and  the  earth  where  any  mass  of  matter  would  weigh  nothing  ? 


CHAPTER   II. 
MOTION. 

IF  all  matter  were  quiescent  there  would  be  no 
changes  anywhere,  for,  as  most  persons  already  know, 
all  the  changing  phenomena  that  make  life  possible  and 
interesting  are  due  to  movements  of  some  kind.  If  the 
world  should  stop  turning  upon  its  axis  there -would  he 
continuous  day  or  night.  If  it  should  stop  its  motion 
about  the  sun  there  would  be  no  change  of  seasons. 
If  the  molecules  should  stop  vibrating  there  would  be 
neither  heat  nor  light,  for  such  motions  constitute  heat 
and  give  rise  to  light,  and  in  the  absence  of  these  all 
life  would  cease  ;  indeed,  the  world  would  be  a  most 
uninviting  place  to  be  in,  even  if  one  could  exist  upon 
it.  If,  then,  all  kinds  of  phenomena  are  caused  by 
motion,  it  is  proper  to  study  the  characteristics  of  it  in 
order  to  discover  how  so  great  a  variety  can  flow 
from  it. 

Motion  means  change  of  position  or  of  place.  It  is  not 
very  easy  to  give  a  definition  that  shall  cover  all  cases. 
Two  pei-sons  in  a  car-seat  may  be  moving  at  the  rate  of 
50  miles  an  hour,  yet  be  no  more  disturbed  by  it  than  if 
they  were  in  a  house.  If  one  walks  backward  upon 
a  train  as  fast  as  the  train  moves  forward,  lie  may  talk 
all  the  time  with  a  man  standing  still  by  the  side  of  the 
track.  With  reference  to  the  standing  man  he  might  be 
still ;  with  reference  to  the  train  he  might  be  walking 


24  NATURAL    PHILOSOPHY. 

four  miles  an  hour.  Motion  is  therefore  relative  ;  that 
is,  it  depends  upon  what  the  moving  body  is  compared 
with.  If  a  man  walks  round  a  tree  facing  the  tree  all 
the  time,  he  has  faced  every  part  of  the  horizon,  he  has 
turned  completely  round.  If  he  walks  round  the  tree 
facing  in  one  direction  all  the  time,  he  will  have  seen 
the  tree  on  one  side  only.  The  moon  constantly  faces 
the  earth  with  the  same  side,  as  if  it  were  fixed  to  the 
end  of  a  rod  connected  with  the  earth.  It  therefore 
turns  upon  its  axis,  although  it  appears  not  to. 

Practically  there  is  little  or  no  difficulty  in  employing 
the  term  motion;  a  moving  body  may  go  fast  or  slowly, 
it  may  go  in  a  straight  or  a  curved  line,  to  and  fro,  or 
round  and  round.  If  one  imagines  a  point  to  have 
motion,  its  direction  and  velocity  may  be  any  assignable 
one.  The  consideration  of  these  gives  rise  to  a  mathe- 
matical science  called  Kinematics. 

KINDS   OF   MOTION. 

I.  Traiislational.  —  A  body  of  any  magnitude  may 
move  in  any  direction  in  free  space,  north  or  south,  east 
or  west,  up  or  down,  or  in  any  intermediate  direction. 
A  body  thus  moving  freely  in  any  direction  is  said  to 
move  in  a  free  path,  no  matter  whether  it  move  a  long 
or  a  short  distance.  Nor  does  it  matter  what  the  size 
of  the  body  may  be :  a  cannon  ball  may  go  through  the 
air  eight  or  ten  miles  without  striking  anything ;  while 
a  molecule  of  air  may  move  no  more  than  the  millionth 
of  an  inch,  before  striking  another  molecule,  yet  this 
distance  would  be  fifty  times  its  own  diameter.  When 
a  body  moves  as  a  whole  from  one  place  to  another 


MOTION. 


25 


with  such  free-path  motion  it  is  said  to  have  translatory 
motion  ;  if  it  goes  in  a  straight  line,  like  a  billiard  ball, 
the  motion  is  called  rectilinear;  and  if  in  a  curved  line, 
like  that  of  a  cannon  ball,  it  is  called  curvilinear  motion. 
The  drifting  of  clouds,  the  flight  of  birds,  of  arrows, 
the  movement  of  meteors,  comets,  and  planets  in  their 
orbits,  are  examples  of  translatory  motion,  arid  the 
student  may  think  of  and  name  others  of  the  same  kind. 

II.  Vibratory.  —  To   and   fro  movements    like    the 
swinging  of  a  clock  pendulum  (Fig.  5),  the  movement 


of  the  piston  of  a  steam-engine,  the  swaying  of  the 
branches  of  a  tree,  the  vibrations  of  the  prongs  of  a 
tuning-fork  (Fig.  6),  the  reeds  and  strings  of  musical 
instruments,  are  examples  of  a  different  kind  of  motion, 
in  which  the  changes  of  position  are  of  the  parts  of  a 
body  with  relation  to  itself  rather  than  to  other  things. 
The  prongs  of  a  tuning-fork  approach  and  recede  from 
each  other,  each  retracing  its  path  —  a  characteristic  of 
what  is  called  vibratory  motion.  If  the  moving  part  be 


26  NATURAL    PHILOSOPHY. 

large,  and  its  motion  conspicuous,  like  the  pendulum 
of  a  clock,  the  motion  is  sometimes  called  oscillatory. 

III.  Rotary.  —  A  body  of  any  size  or  shape  may  be 
made  to  turn  upon  some  axis  or  spin  around  like  a  top 
or  wheel.  In  such  motion  the  parts  of  the  body  do  not 
change  their  relative  positions  with  reference  .to  each 
other,  but  with  reference  to  other  bodies  away  from 
them.  Thus,  every  part  of  a  turning  wheel  is  presented 
each  revolution  to  opposite  points  in  space.  Such 
motions  are  called  rotary  ;  and  examples  of  it  are  to  be 
seen  everywhere. 

No  one  of  these  kinds  of  motion  is  peculiar  to  any 
body.    They  are  applicable  to  masses  of  all  magnitudes. 
An    atom    or   a   molecule    may 
spin   upon  its   axis  as  well  as 
does   the   earth  ;    and    in    gen- 
eral, what  a  body  will  do  depends 
upon  what  kind  of  motion  it  may 
have.     By  spinning  a  base  ball 
it  may  be  made  to  go  through 
the  air  in  a  curved  line  instead 
of  a  straight  one  ;   and  a  spin- 
ning top  (Fig.  7)  will  stand  on  its  point,  which  it  will 
not  do  if  it  be  not  spinning. 

A  vibrating  tuning-fork  or  bell  will  apparently  attract 
small  bodies  to  itself  ;  so  from  the  behavior  of  a  body 
one  may  often  know  what  kind  of  motion  it  has  without 
examining  it  directly. 

These  three  kinds  of  motion  —  translator)/,  vilm/"/-//. 
and  rotary  —  are  the  primary  motions.  All  the  various 


MOTION.  27 

kinds  of  movements  seen  in  machines  are  due  to  these 
ai  id  their  compounds  ;  and  obviously  a  body  may  have 
any  one  or  a  combination  of  them.  A  bullet  let  fall  goes 
in  a  translatory  motion  to  the  ground.  If  it  be  shot 
horizontally  from  a  gun  it  will  go  in  another  translatory 
direction,  which  is  a  compound  of  horizontal  and  vertical 
translatory  motions,  that  is,  its  curved  path  will  be  a 
compound  of  two  translatory  motions.  In  the  diagrams 
on  page  28  are  represented  these  different  kinds  and 
their  combinations. 

I.  A  body  at  A  may  move  on  in  the  direction  AB  for 
an  indefinite  distance. 

II.  The  body  may  move  to  and  fro  between  A  and  B. 

III.  A  point  may  rotate  in  the  same  path  indefinitely. 

IV.  The  resultant  of  two  translatory  motions  AB  and 
AC  upon  a  given  body  at  A  will  make  it  move  in  a 
straight  line  AD,  if  the  velocities  in  the  two  directions 
In'  uniform. 

V.   If  the  velocity  of  one  be  increasing  in  one  direc- 
tion, as  AC,  the  path  taken  will  be  curvilinear,  as  AD. 

VI.  A  body  moving  back  and  forth  over  a  line  like 
AB  in  Fig.  II,  and  given  a  forward  motion  at  right 
angles  to  the  vibratory  movement,  would  make  an 
undulatory  path  which  would  be  a  combination  of 
vibratory  and  translations!  motion. 

VII.  The  motion  of  a  screw  when  worked  into  wood 
is  an  illustration  of  a  combination  of  rotary  and  trans- 
latory motions  ;  the  rotary  in  twisting  the  screw,  and 
the  translatory  in  advancing  into  the  wood.  Also  if 
the  end  of  a  rope  20  or  30  feet  long  be  held  in  the 
hand,  and  the  hand  be  shaken  np  and  down,  a  series  of 


NATURAL   PHILOSOPHY. 


waves  will  travel  along  the  rope,  composed  of  the 
vibratory  and  translatory  motions.  If  the  hand  be 
swung  round  and  round  a  spiral  motion  in  the  rope 
will  be  the  resultant,  as  in  VII. 


TRANSLATORY. 


VIBRATORY. 


ROTARY. 


TRANSLATORY. 


CURVILINEAR. 


UNDULATORY. 


SPIRAL. 


MOTION.  29 

If  one  will  observe  the  various  kinds  of  movements 
that  may  be  seen  in  a  sewing-machine,  he  will  be  able 
to  identify  several  of  the  foregoing :  the  vibratory 
motion  of  the  treadle  ;  the  rotary 'of  the  balance-wheel, 
pulley,  and  spindle  ;  the  vibratory  of  the  needle  and 
shuttle  ;  and  translatory  of  the  thread  and  the  cloth. 
In  like  manner  one  sJiould  trace  the  motions  in  engines, 
looms,  and  other  complicated  machines,  with  the  pur- 
pose of  finding  whether  there  be  any  other  motions 
than  the  ones  described  here  ;  and  if  so,  how  they  are 
composed. 

Kates  of  Motion.  —  The  rate  of  change  of  position 
of  a  body  is  called  its  velocity ;  as  when  we  say  that  a 
man  walks  at  the  rate  of  three  miles  an  hour,  or  that 
the  speed  of  a  bullet  is  1000  feet  per  second.  These 
statements  contain  references  to  both  space  and  time, 
and  make  it  needful  for  us  to  use  some  standard  for 
each.  The  unit  of  length  that  is  most  commonly  used 
is  the  foot ;  if  shorter  spaces  are  being  considered  we 
use  the  inch,  if  long  distances  are  considered  we  use 
the  mile,  which  equals  5280  feet. 

The  standard  of  time  used  everywhere  is  the  second. 
Practically  we  measure  time  in  seconds,  minutes,  hours, 
days,  and  years,  and  whether  we  use  one  or  the  other 
depends  upon  what  the  special  needs  are.  The  year 
—  365  i  days  —  is  the  time  it  takes  for  the  earth  to 
complete  one  circuit  about  the  sun.  The  day  is  the 
time  it  takes  for  it  to  turn  on  its  axis  once.  The  hour 
is  the  twenty-fourth  part  of  the  day,  and  the  minute 
the  sixtieth  part  of  an  hour.  The  second  is  the  time  it 


30  NATURAL   PHILOSOPHY. 

takes  for  a  pendulum  39.117  inches  long  to  vibrate 
once,  and  sixty  such  vibrations  measure  the  time  of  one 
minute,  and  86,400  of  them  are  completed  while  the 
earth  turns  round  once  ;  that  is,  86,400  seconds,  is  the 
measure  of  the  length  of  the  day. 

The  rate  of  translator^/  motion  is  measured  as  a 
distance  per  second,  per  minute,  or  per  hour,  but  it  is 
not  to  be  understood  that  the  motion  is  necessarily 
maintained  through  the  time-period  mentioned.  For 
instance,  when  we  say  that  the  velocity  of  a  bullet  is 
1000  feet  per  second,  it  means  only  that  if  the  motion 
was  maintained  uniform  for  a  second  the  bullet  would 
travel  1000  feet.  It  might  travel  at  the  rate  of  a  1000 
feet  per  second  and  go  only  a  foot.  A  train  of  cars 
might  go  at  the  rate  of  50  miles  an  hour  and  not  travel 
a  mile.  Velocity  is  the  rate  of  motion  at  a  given 
instant.  When  the  rate  is  known,  and  the  time  is 
given,  the  distance  is  found  by  multiplying  the  rate  by 
the  time. 

Let  v  equal  the  rate  and  t  the  time,  then  the 
distance,  d  =  vt.  Any  two  of  these  being  known,  of 
course  the  other  one  can  be  found. 


TAHLE  OF    OBSERVED    VELOCITIES. 

Miles  per  hour. 

Man  walking  .......       3-4 

Horse  trotting 1 1 »-:!() 

Gentle  wind 6 

I'aihvay  train  ......                 50 

Hurricane  100 


MOTION.  31 

Feet  per  second. 
Man  walking  ......  6 

Sailing  vessel     ...."...  15 

Steamships 30 

Crow  flying 40 

Race  horse     .......  42 

Swallow  Hying 134 

Swift  flying 250 

Sound  in  air  .         .         .         .         .         .       1100 

Cannon  ball 2000 

Hydrogen  molecule    ......       6000 

Miles  per  second. 
Shooting  stars  at  earth  .....  22 

Comet  near  the  sun 400 

Light 186,400 

The  rate  of  vibration  means  the  number  of  vibrations 
per  second.  Thus,  a  tuning-fork  may  vibrate  256  times 
a  second ;  the  wings  of  a  duck  3  or  4  times ;  the  wings 
of  a  mosquito  1000  times;  and  the  chirrups  of  crickets 
represent  about  3000  vibrations  per  second.  Piano 
strings  have  a  range  from  40  to  4000.  Steel  rods  have 
been  made  having  a  rate  as  high  as  20,000  per  second. 
In  each  of  these  cases  a  to  and  fro  movement  represents 
one  vibration.  In  general,  the  smaller  a  body  is  the  more 
rapid  is  its  vibratory  rate,  provided  it  have  the  same  form 
and  be  made  of  the  same  material  ;  so  the  extremely 
minute  atoms  of  matter  have  very  high  vibratory  rates. 
A  hydrogen  atom,  when  made  incandescent,  vibrates  not 
less  than  450  millions  of  millions  of  times  in  one  second. 
How  this  is  known  will  be  pointed  out  in  the  chapter 
on  ether  waves. 

Sometimes  it  is  convenient  to  know  th'e  actual  space 
tluit  is  moved  over  by  ;i  vibrating  l>ody  in  terms  of 


32  NATURAL   PHILOSOPHY. 

translator^  motion.  If  the  prong  of  a  tuning-fork 
move  the  hundredth  of  an  inch  each  vibration,  and  if 
it  vibrates  a  hundred  times  per  second,  the  total  distance 
will  be  100  X  T^o  =  1  inch-  The  extent  of  the  swing 
of  any  point  of  a  vibrating  body  on  each  side  of  its 
position  when  at  rest  is  called  the  amplitude;  and  in 
the  above  case  the  amplitude  is  the  four-hundredth  of 
an  inch.  Suppose  then  the  amplitude  of  vibration  of  a 
hydrogen  atom  be  one-fourth  of  its  diameter,  or  two 
hundred-millionths  of  an  inch,  and  that  it  vibrate  500 
millions  of  millions  of  times  per  second,  the  actual 
space  moved  through  in  that  interval  will  be  : 
500,000000,000000 


100,000000 


=  5,000000  inches  =  80  miles. 


Rotary  Speeds  have  wide  ranges,  and  are  measured 
by  the  number  of  revolutions  per  second  or  per  minute. 
A  wheel  may  turn  round  fast  or  slowly ;  the  balance- 
wheel  of  an  engine  may  turn  round  once  a  second  ; 
high-speed  steam-engines  may  turn  four  or  five  times 
per  second ;  small  wheels  have  been  made  to  rotate  800 
times  a  second.  Sometimes,  when  great  accuracy  is 
required  the  velocity  is  measured  in  degrees  per  second. 
For  instance,  if  a  disk  turns  5|  times  per  second,  a 
given  point  in  its  circumference  moves  at  the  rate  of 
360  X  5i  =  1980°  per  second. 

Again,  the  rate  of  rotation  may  be  considered  as  the 
time,  f,  it  takes  to  make  one  revolution.  The  circum- 
ference of  a  circle  of  radius  r  is  2  TT  r  (TT=  3,1416), 
and  when  that  is  described  in  time  t,  with  velocity  v, 
we  have  2irr=ttf;  v  being  the  equivalent  of  trans- 
lational  motion. 


MOTION.  33 

A  driving-wheel  of  a  locomotive  that  is  six  feet  in 
diameter  will  advance  nearly  19  feet  each  revolution. 
If  the  locomotive  is  to  move  at  the  rate  .of  a  mile  a 
minute,  the  wheel  must  turn  round  -|^  =  4.6  times 
per  second.  A  disk  four  inches  in  diameter,  turning 
800  times  a  second,  would  advance  with  a  speed  of 

2frr  X  800 
— — =  837  feet   per  second,    nearly   10    miles 

a  minute. 

QUESTIONS. 

1.  If  the  distance  to  the  sun  be  93,000,000  miles,  what  is  the 
velocity  per  second  of  the  earth  in  its  orbit  ? 

2.  If  the  earth  be  8000  miles  in  diameter,  what  is  the  velocity 
per  hour  of  a  point  on  the  equator  due  to  the  daily  rotation? 

3.  If  the  velocity  of  sound  be  1100  feet  per  second,  how  long 
will  it  take  a  sound  to  go  quite  round  the  earth  ? 

4.  If  a  duck  fly  140  feet  per  second,  how  long  will  it  take  it  to 
fly  from  Labrador  to  Florida? 

5.  A  balance-wheel   ten   feet    in  diameter   revolves   2£  times 
a  second  ;  what  is  the  velocity  of  a  point  upon  the  rim  ? 

G.  If  a  wheel  make  five  rotations  per  second,  what  is  its 
angular  velocity.  ? 

Uniform  and  Varying  Rates  of  Motion.  —  So  far  it 

has  been  assumed  that  the  rate  of  motion  of  each  kind 
was  uniform,  that  is,  it  did  not  change  during  the 
interval  of  time  considered.  We  know,  however,  that 
if  a  ball  be  thrown  into  the  air  it  is  soon  stopped.  It  is 
the  same  with  a  bullet  shot  from  a  rifle,  a  top  set 
spinning,  a  stone  made  to  slide  on  glare  ice,  —  indeed 
every  kind  of  body  having  motion  of  any  kind  given 
to  it  and  left  to  itself  gradually  comes  to  rest.  We 
attribute  to  friction  the  loss  of  motion  on  the  ground 


34  NATURAL    PHILOSOPHY. 

and  in  the  air.  Suppose,  however,  that  there  was 
nothing  to  interfere  with  the  motion,  that  the  body  did 
not  lose  motion  by  imparting  it  to  other  bodies,  how 
long  would  any  body  continue  to  move  under  such  a 
condition  ?  Evidently,  if  it  did  not  give  up  its  motion 
to  anything  else  it  would  go  on  with  the  same  velocity 
indefinitely,  that  is,  its  motion  would  be  uniform. 

A  billiard  ball  goes  in  a  straight  line  until  it  strikes 
something;  it  does  not  turn  from  its  course  unless 
compelled  to  do  so  by  some  other  body  acting  upon  it. 
Neither  does  a  non-living  object  move  itself  in  any 
way.  It  will  remain  where  it  is,  and  as  it  is,  for  an 
indefinite  length  of  time  —  as  long  as  no  other  body 
acts  upon  it.  These  three  facts  have  been  embodied  in 
what  is  called  a  law  of  motion,  namely  :  Every  body 
will  maintain  its  state  of  rest  or  of  uniform  motion  in  a 
straight  line  as  long  as  it  is  not  acted  on  by  another  body. 
This  action  of  bodies  of  all  kinds  and  of  all  sizes  is 
sometimes  called  the  Law  of  Inertia.  It  means  that  in 
the  absence  of  friction  and  impact,  bodies  in  motion 
will  continue  to  move  in  the  same  direction  and  at  the 
same  rate  forever. 

It  is  because  the  earth  is  moving  in  frictionless  space 
that  it  continues  to  rotate  so  regularly  upon  its  axis,  so 
that  the  length  of  the  day  has  not  varied  a  second  in 
2000  years.  Uniform  motion  under  such  conditions 
does  not  imply  that  any  power  or  force  or  pressure  is 
acting  upon  a  body  to  keep  it  going.  Wherever  there 
is  friction,  a  continuous  push  is  needed  to  maintain 
uniform  motion,  and  the  push  must  be  equal  to  the 
frictional  resistance. 


MOTION.  35 

Acceleration.  —  When  the  push  of  another  body 
exceeds  the  frictional  or  other  resistance,  then  the  body 
pushed  has  its  velocity  increased,  and  if  the  pressure 
he  constant  the  increase  in  velocity  is  constant ;  that 
is,  if  a  pressure  of,  say,  five  pounds  will  give  a  body  a 
velocity  of  two  feet  in  one  second,  it  will  give  it  an 
additional  velocity  of  two  feet  the  second  second,  and 
still  another  addition  of  two  feet  the  third  second,  and 
so  on.  That  is  to  say,  the  velocity  will  be  proportional 
to  the  time  the  pressure  is  maintained.  In  such  a  case 
the  rate  of  increase  in  velocity  is  called  acceleration,  which 
in  the  above  example  is  two  feet.  If  the  pressure  were 
greater  the  acceleration  would  be  greater.  A  body 
with  an  acceleration  of  two  feet  per  second  will  have  a 
velocity  of  four  feet  at  the  end  of  the  second  second, 
and  twenty  feet  at  the  end  of  the  tenth  second. 

If  we  let  v  equal  velocity,  t,  time,  and  «,  acceleration, 

then  v  =  at  and  a  =  -  • 

Gravity  produces  acceleration  upon  falling  bodies. 
It  is  found  by  experiment  to  give  a  velocity  of  32.2  feet 
per  second  to  any  freely  falling  body;  hence,  if  a  body 
falls  for  two  seconds  its  final  velocity  is  64.4  feet,  and 
so  on.  The  letter  g  is  commonly  employed  to  represent 
the  acceleration  of  gravity,  and  in  the  above  expression 
would  take  the  place  of  a,  which  then  would  read  v  =  gt. 
This  will  be  the  meaning  of  the  letter  g  hereafter,  and 
its  numerical  value  will  be  32.2  feet.  Of  course  gravity 
retards  the  velocity  of  a  body  thrown  up  into  the  air, 
and  its  retarding  pull  subtracts  from  the  velocity  of  an 
ascending  body  32.2  feet  for  every  second.  This  is 


36  NATURAL    PHILOSOPHY. 

called  negative  acceleration.  It  is  found  by  experiment 
that  a  body  falling  from  rest  during  one  second  falls 
but  16.1  feet  while  it  is  acquiring  a  final  velocity  of 
32.2  feet.  Its  average  velocity  for  the  whole  second  is 
one  half  its  final  velocity.  In  like  manner  the  average 
velocity  of  a  falling  body  for  any  time  is  half  its  final 

velocity,  or  ^— •  Thus,  a  body  falling  from  rest  for 
five  seconds  will  have  a  final  velocity  of  gt  =  32.2  X  5 

,  1  R~l 

=  161  feet,  and  an  average  velocity  of  ^—  =  ——-  =  80.5 
feet.  If  it  falls  for  ten  seconds,  gt  =  322  feet,  and  its 
average  velocity  is  $-  =  161  feet,  and  so  on  for  any  value 

of*. 

The  space,  s,  that  a  falling  body  will  move  through 
will  be  equal  to  its  average  velocity  multiplied  by  the 

time,  ^-Xt. 

Thus,  if  the  body  fall  for  five  seconds  its  average 
velocity  will  be  £—  —  80.5  feet,  and  the  space  s  will 

^e  9  X  t  —  402.5  feet.  If  it  fall  for  ten  seconds  its 
average  velocity  will  be  ^—  =  161,  and  the  space  « 

will  be  -^  X  t  —  1610  feet. 

In  this  the  prime  factor  t  appears  twice,  and  it  is 
customary  to  write  the  expression  thus,  s  =  ^- ,    and 

to  say  that  the  space  passed  over  by  a  falling  body  is 
proportional  to  the  square  of  the  time.  The  same  law 


MOTION.  37 

holds  true  for  any  other  constant  pressure  or  accelera- 
tion in  any  direction,  and  a,  acceleration,  may  be  sub- 
stituted for  (j  in  the  formula  ;  thus,  —  =  average 

velocity,  and  -— -  X  t  =  *,   space  passed  over.      For 

example,  a  constant  pressure  gives  an  electric  car  an 
acceleration  of  5  feet  per  second,  what  is  its  velocity 
in  8  seconds,  and  how  far  will  it  have  moved? 

Ans,  at  =  5  X  8  =  40  feet  per  second,  8  =  —  X  t 
=  5_><_?x  8  =  160  feet. 

It  is  to  be  understood  that  in  all  practical  problems 
of  moving  bodies  in  the  air,  the  air  itself  acts  to  retard 
somewhat  their  movements.  The  value  of  g  as  given, 
32.2  feet,  represents  the  velocity  that  a  body  falling  in 
a  vacuum  wrould  acquire.  Above  the  atmosphere  there 
is  nothing  to  retard  motions,  and  meteors  acquire  a 
very  high  velocity  (25  or  more  miles  a  second),  and 
when  they  reach  the  atmosphere  on  their  way  to  the 
earth,  the  friction  is  so  great  as  to  set  them  afire,  which 
shows  itself  in  the  glow  in  their  path.  This  high  ve- 
locity is  not  due  to  the  earth  alone,  but  to  the  sun  also. 
As  the  sun  is  much  larger,  its  attractive  power  is 
greater,  and  therefore  the  value  of  g  at  the  sun  is 
about  28  times  its  value  at  the  earth,  that  is,  about  900 
feet.  A  body  drawn  to  the  sun  may  have  a  velocity  of 
400  miles  per  second,  the  highest  translational  velo- 
city known. 

The  curvature  of  the  earth  is  8  inches  to  the  mile, 
that  is,  if  a  long  straight  horizontal  line  were  to  touch 


38  NATUKAL    PHILOSOPHY. 

the  smooth  surface  of  a  large  body  of  water,  like  a  lake 
or  ocean,  it  would  be  eight  inches  away  from  the  sur- 
face at  the  distance  of  a  mile.  If,  then,  above  the 
atmosphere,  one  were  to  shoot  a  rifle  ball  in  a  horizontal 
direction  with  such  velocity  that  it  would  go  a  mile 
while  the  body  were  falling  eight  inches,  the  ball  would 
be  no  nearer  the  earth  than  when  it  started,  and  if  not 
retarded  by  friction  it  would  continue  on,  quite  round 
the  earth,  —  would  indeed  become  a  satellite.  Can  you 
compute  what  the  velocity  would  have  to  be  ? 

QUESTIONS. 

1.  If  a  body  could  be  shot  off  in  free  space,  beyond  the  atmos- 
phere, what  would  be  its  direction,  and  what  its  change  of  velocity, 
if  any? 

2.  If  a  body  move  with  uniform  velocity  144  feet  in  three 
seconds,  what  is  its  velocity  per  second  ? 

3.  A  body  has  an  acceleration  of  five  feet,  what  will  be  its 
velocity  at  the  end  of  five  seconds?     What  will  be  the  whole 
distance  passed  over?    What  will  be  its  velocity  at  the  end  of  the 
third  second  ?    What  space  will  it  pass  over  during  the  last  second  ? 

4.  If  a  body  be  tossed  up  into  the  air  with  a  velocity  of  32.2 
feet  per  second,  how  long  a  time  will  it  continue  to  rise?     How 
high  will  it  rise?     How  loug  will  it  remain  in  the  air? 

5.  How  long  will  it  take  a  body  to  fall  1000  feet,  ignoring  the 
resistance  of  the  air? 

6.  If  a  bullet  were  shot  vertically  upwards  with  a  velocity  of 
900  feet  per  second,  how  high  would  it  rise,  and  how  long  would 
it  be  rising? 

7.  If  the  same  thing  should  be  done  at  the  sun,  how  high 
would  it  rise,  and  for  how  long  ? 

8.  Find  what  the  velocity  of  the  moon  is  in  its  orbit  at  the 
distance  of  240,000  miles. 


CHAPTER    III. 
WORK. 

A  f  push  or  a  pull  may  be  measured  in  pounds.  A 
spring  balance  answers  both  for  weighing  things  — 
finding  gravitative  pressure  —  and  for  measuring  pres- 
sure in  any  other  direction.  The  amount  of  pull  is 
indicated  in  pounds  and  fractions  of  a  pound  upon  the 
scale.  If  the  pressure l  results  in  the  movement  of  the 
body  pulled,  work  has  been  done ;  if  the  body  does  not 
move,  no  work  has  been  done.  The  amount  of  work  is 
equal  to  the  pressure  measured  in  pounds  multiplied  by 
the  distance  in  feet,  and  the  product  is  called  foot-pounds. 
Thus,  suppose  that  to  move  a  carriage  it  requires  a 
pressure  of  20  pounds.  If  that  pressure  be  maintained 
and  the  carriage  be  moved  ten  feet,  then  20  X  10  =  200 
foot-pounds  of  work  has  been  done.  Unless  the  carriage 
moves  there  is  pressure,  but  no  work.  This  is  the  sense 
in  which  the  term  is  used  in  physical  science.  If  we 
let  p  stand  for  pressure  in  pounds,  d  stand  for  distance 
in  feet,  and  W  for  work,  then  pd  =  W  in  foot-pounds. 

If  a  pound  weight  rests  on  the  table,  its  pressure  is 
constant  there,  but  if  the  weight  be  raised  a  foot,  the 
pressure  will  be  constant  through  the  distance  of  a  foot, 

1  The  word  pressure  is  substituted  for  the  word  force,  which  is  common  in 
other  books,  thus  gravitative  pressure  instead  of  the  force  of  gravitation.  There 
are  many  definitions  and  indefinite  suggestions  to  the  word  force,  while  in 
physics  it  means  what  is  meant  by  the  word  pressure,  which  word  has  no 
abstract  implication. 


40  NATURAL    PHILOSOPHY. 

and  a  foot-pound  of  work  will  be  done.  Hence  10 
pounds  raised  1  foot  is  the  same  in  work  as  1  pound 
raised  10'feet. 

If  a  man  weighing  150  pounds  walks  upstairs  10  feet 
he  has  done  1500  foot-pounds  of  work.  If  a  hod-carrier 
carries  100  pounds  of  brick  up  a  ladder  20  feet  he  has 
done  100  X  20  =  2000  foot-pounds,  aside  from  that 
represented  by  his  own  weight  raised  the  same  distance ; 
whether  he  goes  fast  or  sloV  makes  no  difference  in  the 
amount  of  work  done. 

Power  has  to  do  with  the  rate  at  which  tcork  is  done, 
and  rate  implies  time.  The  unit  of  time  is  the  second, 
and  the  amount  of  work  to  be  done  in  a  second  has 
been  set  by  the  demands  of  business  and  is  known  as 
the  horse-power.  It  equals  550  foot-pounds  per  second 
or  33,000  per  minute.  Hence, 
Pressure  in  pounds,  p,  X  distance  in  feet  per  second,  d, 

550 

=  horse-power.  For  example  :  Suppose  a  pair  of 
horses,  by  pulling  200  pounds  steadily,  is  able  to  move 
a  car  at  the  rate  of  five  feet  a  second,  how  much  power 
is  spent  ? 

200  X  5       t  Q  . 
Ans.   — — - —  =  1.8  horse-power. 

550 

Whether  the  pulling  was  done  by  horses,  steam- 
engine,  or  electric  motor  would  make  no  difference  in 
this,  so  both  steam-engines  and  electric  motors  are 
rated  in  horse-power. 

From  the  above  principles  it  may  be  seen  that  no 
matter  how  large  a  body  may  be,  nor  how  fast  it  may 


WORK.  41 

move,  if  it  produces  no  pressure  upon  another  body  it 
does  no  work ;  also  that  friction,  which  is  the  resistance 
to  motion  of  surfaces  in  contact,  is  proportional  to 
pressure,  as  it  may  be  measured  in  foot-pounds.  A 
body  like  the  moon  may  continue  to  go  round  the  earth 
indefinitely  long,  though  there  is  no  pressure  acting. 

If  a  ten-pound  weight  rests  upon  the  ground  it  does 
no  work,  yet  if  a  man  holds  it  up  for  a  time  it  tires  him, 
and  he  is  conscious  of  having  done  work  in  the  physical 
sense,  although  he  has  held  it  quietly.  The  explanation 
is  that  when  muscles  are  stretched  they  begin  to  vibrate 
longitudinally,  a  great  many  times  a  second.  As  they 
lengthen  the  weight  falls  slightly,  as  they  contract  it  is 
pulled  up,  and  thus  the  effect  is  the  same  as  though 
one  had  raised  and  lowered  the  weight  successively  at 
a  slower  rate.  As  one  walks  his  body  rises  and  falls 
regularly;  his  muscles  therefore  do  work  in  raising  his 
body  an  inch  or  two  each  step,  and  after  a  time  he 
becomes  weary.  Suppose  he  raises  his  body  of  150 
pounds  two  inches  each  step,  and  that  he  steps  twice  a 
second,  he  is  doing  1|°  =  25  foot-pounds  of  work  each 
step,  50  foot-pounds  each  second,  equal  to  ^j  —  JT  of 
a  horse-power.  In  flight,  birds  propel  themselves 
through  the  air  by  beating  it  with  their  wings,  and 
thereby  producing  pressure  and  doing  work.  If  a  large 
bird  like  a  goose  were  flying  at  the  rate  of  thirty  miles 
an  hour,  which  is  equal  to  44  feet  a  second,  and  if  a 
continual  pressure  of  one  pound  were  maintaining  that 
speed,  it  would  be  expending  44  foot-pounds  of  work 
per  second,  nearly  one-twelfth  of  a  horse-power.  It  is 
not  probable  that  the  pressure  would  be  nearly  so 


42  NATURAL   PHILOSOPHY. 

much ;  and  if  it  were  but  one  ounce,  the  goose  would 
be  expending  ||  =  2.75  foot-pounds  per  second,  the 
two-hundredth  of  a  horse-power. 

QUESTIONS. 

1.  How  much  work  is  done  in  pushing  a  cart  a  mile  if  the 
pressure  be  10  pounds  ? 

2.  How  much  work  do  you  individually  do  in  climbing  a  hill 
500  feet  high? 

3.  If  a  squirrel  carries  five  pounds  of  nuts  to  his  storehouse 
fifty  feet  up  a  tree,  how  much  work  does  he  do? 

4.  A  wagon  is  loaded  with  stones  that  have  to  be  raised  five 
feet ;   if  the  load  weighs  1000  pounds  how  much  work  was  ex- 
pended in  loading  it  ? 

5.  The  pull  of  a  locomotive  upon  a  train  going  30  miles  an 
hour  is  2000  pounds,  what  horse-power  is  expended  ? 

6.  The  balance-wheel  to  an  engine  doing  40  horse-power  of 
work  is  revolving  four  times  a  second  and  is  ten  feet  in  diameter, 
what  is  the  pull  upon  the  belt? 

7.  If  a  pound  weight  be  tossed  up  16  feet  high,  how  much 
work  is  represented?     What  initial  velocity  is  needed  to  make  it 
rise  16  feet? 

8.  If  a  bullet  weighing  an  ounce  be  shot  vertically  upwards 
with  an  initial  velocity  of  1000  feet  per  second,  how  high  will  it 
rise,  and  how  much  work  will  be  spent  on  it? 

9.  If  a  laborer  shovels  six  pounds  of  dirt  each  shovelful,  and 
ten  of  them  per  minute,  into  a  cart  six  feet  high,  at  what  rate  is 
he  doing  work  ? 

10.  A  pressure  of  two  pounds  is  needed  upon  the  crank  of  a 
grindstone  that  has  a  radius  of  one  foot.     If  it  be  turned  twice  a 
second,  how  much  power  will  be  spent  ? 

11.  If  atoms  be  the  fifty-millionth  of  an  inch  in  diameter,  at 
what  rate  per  second  are  they  assembled  and  arranged  in  a  stalk 
of  asparagus,  half  an  inch  in  diameter,  that  grows  six  inches  in 
length  in  a  day  ? 


CHAPTER   IV. 

ENERGY. 

BY  energy  is  meant  ability  to  produce  pressure. 
Wherever  there  is  pressure  of  any  kind  there  is  energy, 
and  where  the  pressure  produces  motion,  it  does  work 
in  the  mechanical  sense  —  a  pressure  multiplied  by  a 
distance.  The  pressure  of  the  wind  upon  the  sails  of  a 
vessel  or  of  a  windmill  causes  the  one  to  move  forward 
and  the  other  to  rotate.  The  pressure  of  water  causes 
the  water-wheel  to  turn,  the  pressure  of  steam  causes 
the  piston  to  move  forward,  the  pressure  of  an  electric 
current  causes  the  armature  of  an  electric  motor  to 
rotate,  and  the  amount  of  work  is  proportional  to  the 
pressure. 

When  a  body  is  subject  to  two  equal  and  opposite 
pressures  it  cannot  move,  of  course.  A  paper-weight 
lying  on  the  table  presses  upon  the  table,  and  the  table 
presses  upward  upon  the  weight  equally  ;  and  this  con- 
dition of  two  equal  and  opposite  pressures  on  a  body, 
wherever  it  occurs,  is  called  equilibrium,  and  no  motion 
results.  If  the  weight  were  free  to  fall,  that  is,  if  the 
tuUe  pressure  were  removed,  the  gravity  pressure 
would  still  remain,  and  it  then  could  do  an  amount  of 
work  proportional  to  the  distance  it  could  fall.  If  it 
weighed  one  pound  and  could  fall  three  feet  it  would 
do  three  foot-pounds  of  work  ;  if  the  weight  could  fall 
25  feet  it  could  do  25  foot-pounds,  and  so  on. 


44  NATURAL    PHILOSOPHY. 

There  are  many  cases  of  equilibrium  where  there  is 
pressure,  but  no  motion  is  apparent.  A  clock  wound 
up  with  pendulum  stopped,  a  steam  boiler  with  valves 
closed,  water  in  any  containing  vessel,  a  magnet  with 
armature  held  near  it,  are  common  examples.  The 
energy  in  these  cases  is  called  potential  energy.  When 
a  given  pressure  upon  a  body  is  not  balanced  by  an 
opposite  one,  the  body  moves,  and  may  do  work.  The 
energy  of  a  moving  body  is  called  kinetic  energy. 

Rate  of  Work.  —  Wherever  work  is  being  done  it  is 
done  at  some  rate  which  implies  time,  and  it  is  often 
convenient  to  know  what  the  working  power  of  a 
moving  body  is  when  we  know  only  its  weight  and 
velocity. 

We  have  seen  that  if  a  body  be  tossed  up  into  the  air 
with  a  velocity  of  32  feet  per  second,  it  will  rise  16 
feet ;  if  the  body  weighed  a  pound  then  the  work 
done  on  it  would  be  16  foot-pounds,  for  it  represents  a 
weight  of  one  pound  raised  16  feet.  If  the  initial 
velocity  were  doubled  and  made  64  feet  per  second, 
then  the  body  would  rise  to  the  height  of  64  feet. 
64  foot-pounds  of  work  would  be  done  by  doubling  the 
velocity,  and  64  is  four  times  16 ;  that  is,  by  doubling 
the  velocity  the  amount  of  work  has  been  increased 
four  times,  hence  we  say  that  the  work  a  body  will  do 
is  proportion al  to  the  square  of  its  velocity.  Evidently 
a  pound  falling  16  feet  will  do  16  foot-pounds  of  work, 
for  it  would  raise  a  pound  16  feet  high,  and  in  falling 
64  feet  it  will  do  64  foot-pounds.  Now,  the  distance  a 
body  will  fall  in  any  time  is  equal  to  the  square  of  its 


ENERGY.  45 

final  velocity  divided  by  twice  the  value  of  gravity,  g. 
Distance,  d  =  -—- 

%g 

On  page  21  it  is  shown  that  the  weight  of  a  body  is 
a  variable  quantity,  and  consequently  its  pressure  varies 
with  its  place  on  the  earth.  If  the  weight  of  a  l>ody  be 
divided  by  the  value  of  g  wherever  it  may  chance  to 
be,  we  have  an  invariable  quantity,  which  is  called  the 
mass  of  the  body. 

w 

—  =  m,  and  w  =  me/  ; 

9 

that  is,  the  weight  of  a  body  is  equal  to  its  mass,  w, 
multiplied  by  the  value  of  p. 

The  product  of  the  weight  of  a  body,  which  represents 
its  pressure,  into  its  distance  moved  against  gravity, 

V2 

pd,  =  work  =  W;  p  =  w  —  mg;  d  —  —  • 

Using  these  values  of  p  and  d  we  have 

v2        mv2  7    .     /.    _,  , 

mg  X  ^—  =    o  -  =  work  in  foot-pounds  ; 

tli at  is,  the  work  is  equal  to  one-half  the  product  of  the 
mass  into  the  square  of  the  velocity,  and  this  quantity 
represents  the  energy  which  a  mass  m  has  when  its 
velocity  is  v.  One  must  keep  in  mind  that  m  is  not  in 
pounds,  for  a  pound  weight  has  32.2  units  of  mass 

hence  a  unit  mass  is  ~n  9  °f  a  pound  or  about  half 

an  ounce.      If  we  now  substitute  for  m  its  equivalent 

w    .  ?rr2 

-  in   the  expression,  we  have  =  energy,  and  one 

ij  **  y 


46  NATURAL    PHILOSOPHY. 

may  compute  how  much  work  any  body  may  do  that 
has  a  known  weight  and  velocity.     For  example  : 

A  body  weighing  100  pounds  has  a  velocity  of  25 
feet  per  second,  how  much  energy  has  it? 

wv*      100  x  252      62500 
AnS'          =  -~:     "-    -  976  foot-pounds. 


Vibratory  Energy.  —  So  far  energy  of  translatory 
motions  has  been  considered  ;  but  if  a  body  vibrates  like 
a  tuning-fork  it  has  energy,  for  if  a  light  body  be  made 
to  touch  one  of  the  prongs  it  will  be  beaten  away. 
cab  However,  different  forks  may  have  differ- 
;  ent  rates  of  vibration,  and  each  one  may 
.'  have  varying  degrees  of  amplitude  or  swing. 
;  Suppose  a  fork  vibrates  100  times  a  second, 
and  that  its  amplitude  of  vibration,  a  b  (Fig. 
8),  be  the  hundredth  of  an  inch.  A  com- 
plete vibration  being  the  to-and-fro  move- 
ment, the  complete  distance  moved  for  one 
vibration  will  be  from  b  to  c  to  b  again,  the 
twenty-fifth  of  an  inch  ;  a  hundred  vibra- 
tions will  make  100  X  ^  =  4  inches  per 
FIG.  s.  second.  Here  both  the  number  of  vibra- 
tions n  and  the  amplitude  a  of  each  gives  the  velocity 
v,  and  energy  varies  as  the  square  of  the  velocity,  or 
in  this  case  as  w2a2,  and  in  problems  involving  vibratory 
movements  it  will  not  be  sufficient  to  take  simply  the 
number  of  vibrations  for  the  velocity,  so  vibratory 


energy  will  be  represented  by  — - —  or 


ENERGY.  47 

Kotary  Energy.  —  If  an  iron  rod  a  foot  long  and  an 
inch  thick  were  to  be  given  a  translatory  velocity 
lengthwise  of,  say,  10  feet  a  second,  it  would  have  a 
definite  amount  of  energy.  Suppose  the  rod  were 
curved  into  a  ring,  and  made  to  spin  around  an  axis  in 
the  middle  of  the  ring  at  such  a  rate  that  a  point  on  it 
moved  10  feet  a  second,  its  energy  would  be  the  same 
as  before,  because  there  was  the  same  mass  moving  with 
the  same  velocity  ;  but  it  would  not  be  advancing, 
because  its  motion  was  rotary.  Given  the  number  of 
rotations  a  body  may  make  per  second,  its  weight  and 
diameter  if  it  be  a  wheel  or  a  disk,  one  may  compute 
the  corresponding  velocity  as  if  it  were  translatory,  and 
determine  the  energy.  Thus,  a  wheel  ten  inches  in 
diameter  weighs  25  pounds,  and  has  most  of  its  weight 
in  its  rim.  If  it  revolves  ten  times  a  second,  how 
much  energy  has  it  ? 

Ana.    w'  =  25, 

v  =  10  X  3.14  X  10  =  ^  =  26.1  ft.  per  sec. 
W       25  X  26.12 


64 


=  2b6  foot-pounds. 


QUESTIONS. 


1.  If  a  body  weighing  10  pounds  be  shot  vertically  upward 
with  a  velocity  of  96  feet  per  second,  how  much  work  has  been 
done  on  it  ?     How  much  work  will  it  do  when  it  falls  ? 

2.  If  you  were  to  catch  a  brick  weighing  6  pounds  that  had 
been  tossed  up  10  feet  to  you,  how  much  energy  would  the  brick 
have?     Would  you  be  conscious  of  expending  energy  in  holding 
it  ?     What  kind  of  energy  would  you  say  the  brick  had  ?    Were 
you  to  drop  it,  what  amount  of   energy  would    it   have  5  feet 


48  NATURAL    PHILOSOPHY. 

below  ?  If  it  were  to  be  stopped  there  and  again  dropped,  would 
it  make  any  difference  in  the  whole  amount  of  energy  the  brick 
had  or  the  amount  of  work  it  could  do  ? 

3.  If  a  ton  of  water  falls  10  feet,  how  much  work  is  it  capable 
of  doing  ? 

4.  What  velocity  does  water  acquire  in  falling  20  feet? 

5.  A  certain  stream  has  5  tons  of  water  going  each  minute  over 
a  fall  30  feet  high  ;  what  horse-power  does  it  represent  ? 

6.  A  meteor  weighing  1  pound  comes  into  the  atmosphere  at 
the  rate  of  25  miles  per  second  ;  how  much  energy  has  it  ?     Tf  it 
was  applied  to  lift  a  ton  weight,  how  high  would  it  raise  it  ? 

7.  A  cannon  ball  has  a  velocity  of  1000  feet  per  second.     If  it 
weighs  500  pounds,  how  much  energy  has  it  ?    How  long  would  it 
maintain  a  horse-power  if  it  could  be  applied  ? 

8.  If  a  person  weighing  150  pounds  runs  upstairs  at  the  rate 
of  4  feet  per  second,  what  horse-power  does  the  work  represent  ? 

9.  If  a  person  weighing  1G()  pounds  jumps  6  feet  high,  how 
much  work  does  he  do  ?     If  he  reaches  that  height  in  a  second, 
what  horse-power  does  he  expend  ? 

10.  The  rim  of  a  balance-wheel  is  10  feet  in  diameter  and 
weighs  5  tons.     If  it  be  driven  around  4  times  a  second,  hmv  much 
energy  will  it  have  ? 

(I^OTE.  —  The  use  of  a  balance-wheel  is  to  supply  energy 
for  a  short  time  when  for  any  reason  the  engine  fails  to  keep  up 
the  speed.) 

11.  A   pile-driver   weighing    2500   pounds    falls    15    feet    and 
strikes  the  head  of  a  pile;  what  velocity  does  it  have,   and  ho\\ 
much  energy  ? 

12.  A  10-horse-power  engine  can  lift  15  tons  to  what  height  in 
30  seconds  ? 

13.  A  loaded  wagon  weighing  a  ton  is  drawn  np  a  hill  a  mile 
long,  the  top  of  the  hill  is  2000  feet  higher  than   its  base.      Mow 
much  work  is  done?     Would  it  make  any  difference  \\lietlier  it 
is  drawn  by  horses  or  by  a  steam-engine  V   \\liether  it  were  done 
quick  or  slow  ? 


CHAPTER   V. 

MACHINES. 

WHENEVER  it  is  desirable  to  transfer  pressure  from 
one  place  to  another,  we  employ  a  device  which  we  call 
a  machine.  When  a  weight  like  a  stone  is  raised  with 
a  crowbar,  the  pressure  that  is  applied  at  one  end  is 
transferred  to  the  other  and  utilized  there.  The  bar 
acts  to  transfer  and  change  the  direction  of  the  pressure 
by  means  of  the  support  provided  called  a  fulcrum  a ; 


FIG.  9. 

for  when  the  pressure  is  downward  at  p  it  is  upward 
at  w.  Such  a  machine  is  called  a  lever,  and  the 
principle  of  work  applies  to  it.  Thus,  if  at  p  there 
be  a  downward  pressure  of  10  pounds  continued 
through  one  foot,  then  10  foot-pounds  of  work  have 
been  clone  at  the  other  end  of  the  lever,  whether  it  be 
long  or  short.  In  any  case,  the  product  of  the  weight 
(pressure)  at  w  into  the  distance;  it  is  raised  will  be 
equal  to  the  foot-pounds  of  work  spent  at  p.  The 


50  NATURAL    PHILOSOPHY. 

actual  distance  w  will  rise  depends  upon  the  relative 
lengths  of  the  parts  ap  and  aw.  If  a p  be  twice  as 
long  as  a  w,  the  distance  p  will  move  will  be  twice  the 
distance  that  w  will  move. 

Suppose  a  lever  p  w,  four  feet  long,  has  a  fulcrum  at 
a  one  foot  from  w,  and  that  at  w  is  a  weight  of  50 
pounds,  what  pressure  at  p  will  be  required  to  balance 
w? 

Ans.  Length  a  w  X  w  =  length  a  p  X  P  ;  length 
a  w  —  1 ;  length  a  p  .=  3  ;  1  X  50  =  3  X  P  ;  P  =  -^°- 
=  16.66  pounds. 

Again;  if  pressure  at  p  be  continued  through  a  foot, 
to  what  distance  will  w  be  raised? 

Ans.  Work  at  p  =  work  at  w ;  that  is,  pd  is  the 
same  at  both  places;  hence  16.66  X  1  =  50  X  d. 

,      16.66    ,     , 
a  =  — — —  ot  a  toot. 
50 

The  product  of  the  pressure  into  the  distance 
through  which  it  is  maintained,  will  give  the  work 
done  at  the  other  end  of  the  lever.  Any  amount  of 
work  done  at  one  end  of  a  lever  will  do  an  equal 
amount  of  work  at  the  other  end.  Examples  of  the 
lever  are  very  common,  —  the  claw-hammer,  pincers, 
scissors,  the  weighing  balance,  and  the  steelyard. 
These  and  others  may  be  thought  out  witli  reference 
to  the  above  principles. 

The  pulley  is  a  machine  for  changing  the  direction 
of  a  pressure  with  a  rope  or  belt.  In  its  simplest  form 
it  consists  of  a  grooved  wheel  around  which  a  rope 
may  be  passed  (Fig.  10).  It  is  used  for  conveniently 
lifting  bodies  to  considerable  heights  by  a  continuous 


MACHINES. 


51 


pull  or  pressure  at  one  end  of  the  rope  ;  the  weight  a 
will  be  balanced  by  an  equal  weight  or  pull  upon  the 
other  end  of  the  rope  b,  and  if  the  pressure  upon  b 
be  downward,  of  course  it  does  work  equal  to  pel  upon 
the  weight  a.  If  two  pulleys  be  used,  and  one  end  of 
the  rope  be  made  fast,  as  at  d  (Fig.  11),  then  half  of 


the  weight  of  w  is  supported  by  the  beam,  and  to  raise 
the  weight  w  one  foot  the  rope  at  p  must  be  pulled 
through  two  feet ;  so  by  pulling  50  pounds  two  feet  it 
becomes  possible  to  raise  100  pounds  one  foot. 

Can  you  devise  a  pulley-  arrangement  by  which  a 
man  may  raise  himself  to  any  height? 

Transference   of   Pressure    and    Power.  —  In    the 

pulley  we  have  the  translatory  motion  of  the  rope  in  the 
direction  of  the  pressure,  changed  into  rotary  motion. 
In  the  wheelbarrow  and  in  common  carriages  there  is 


52  NATURAL   PHILOSOPHY. 

translatory  motion  changed  into  rotary,  and  in  the  loco- 
motive rotary  motion  of  the  drivers  changed  to  trans- 
latory of  the  whole  engine,  also  oscillatory  of  the  piston 
into  rotary  and  various  others.  In  the  sewing-machine 
it  is  plain  how  one  kind  of  motion  is  changed  into 
another  kind  with  the  corresponding  pressures.  The 
various  levers,  pulleys,  and  other  parts,  act  to  transfer 
the  pressure  from  the  feet  where  it  begins  on  the 
machine  to  the  active  needle  and  shuttle,  and  at  the 
same  time  to  give  to  them  their  appropriate  motions. 

The  combination  of  pulley  and  belt  is  the  chief 
mechanism  in  machine  shops,  and  factories,  for  the 
distribution  of  power  to  the  various  machines.  They 
deliver  pressure  or  mechanical  power,  and  no  more 
than  is  given  to  them.  They  add  nothing  to  energy, 
but  always  subtract  somewhat  .from  it  because  of 
their  necessary  friction.  In  a  machine  shop  the  power 
to  run  the  machines  when  none  of  them  are  doing 
their  appropriate  work  is  generally  much  greater 
than  that  required  for  their  work.  The  amount  of 
work  a  belt  can  carry  depends  upon  its  velocity. 
Suppose  a  belt  when  running  maintains  a  constant  pull 
of  100  pounds.  If  it  moves  at  the  rate  of  50  feet  per 
second  it  transmits,  pd  =  100  X  50  =  5000  foot- 
pounds in  that  time  ;  if  it  runs  25  feet  per  second  it 
transmits  but  one-half  of  that. 

The  furnace  of  a  steam-engine  is  a  machine  for  trans- 
ferring the  energy  of  fuel  to  the  boiler ;  the  boiler  and 
pipes  transfer  it  to  the  engine,  the  engine  to  the 
shafting  by  belts,  and  the  pulleys  on  the  shafting  to  the 
individual  lathes,  planers,  looms,  or  whatever  kind  they 


MACHINES.  58 

may  chance  to  be.  From  beginning  to  end  it  is  a  pres- 
sure, energy,  the  power  to  do  work  in  one  form  or 
another,  that  is  modified  in  direction  or  form  or  rate 
by  the  various  devices  by  which  it  is  distributed,  and 
which  are  called  machines. 

Transformation  of  Motion. —  When  one  kind  of 
motion  is  changed  into  another,  as  translatory  into 
rotary,  the  resultant  is  called  transformed  motion,  and 
some  kind  of  machine  is  always  needed  to  effect  the 
transformation.  The  quick  unwinding  of  the  string  in 
translatory  motion  gives  the  top  its  spin.  The  rotating 
wheels  of  a  locomotive  give  to  it  its  forward  translatory 
motion.  The  oscillations  of  the  piston  give  rotation  to 
the  wheels,  and  the  continuous  pressure  of  the  steam, 
due  also  to  its  molecular  motions,  is  transformed  into  the 
oscillatory  motion  and  pressure  of  the  piston  in  the 
cylinder.  Another  study  of  the  sewing-machine  will  give 
one  a  good  idea  of  the  mechanism  by  which  one  kind  of 
motion  is  transformed  into  another;  and  it  is  a  capital 
exercise  to  invent  ways  for  thus  transforming  one  kind 
of  motion  into  another  of  a  given  kind.  All  the  various 
tliing-s  done  by  machines  are  brought  about  by  changes 
in  the  character  of  the  motion  of  the  various  parts. 
The  weaving  of  carpets  and  of  cloths  with  intricate 
patterns  goes  on  in  a  loom  in  an  automatic  way  that  is 
wholly  mechanical,  though  it  looks  as  if  there  were 
intelligence  directing  the  various  parts.  There  is  no 
movement  requiring  skill  of  the  hands  but  can  be 
duplicated  by  machinery  ;  even  the  piano-touch  of  a 
skillful  musician  is  but  a  mechanical  movement  varying 


54  NATURAL   PHILOSOPHY. 

in  muscular  quickness,  pressure,  and  release  at  proper 
times,  and  can  be  done  by  a  machine  having  a  proper 
degree  of  perfection.  If  a  mechanically  played  piano 
is  not  satisfactory  music  now,  it  is  because  the  mechan- 
ism is  not  perfected.  Study  the  action  of  a  piano-key 
and  see  if  this  conclusion  is  not  warranted.  Do  you 
think  that  with  a  motion  of  your  finger  you  can  produce 
any  motion  that  mechanism  could  not? 

These  mechanical  principles  are  not  restricted  to 
masses  of  matter  of  definite  or  visible  size,  but  are  as 
applicable  to  microscopic  particles,  molecules,  and 
atoms  as  well,  so  that  exchanges  of  energy  among 
them  take  place  whenever  there  is  a  change  in  the 
character  of  the  motions.  For  convenience,  we  speak 
of  the  motions  of  masses  of  visible  magnitude  as 
mechanical  motions,  to  distinguish  them  from  such  as 
are  too  minute  to  be  seen,  which  are  called  molecular  or 
atomic  motions.  Thus  the  motions  of  an  engine,  of  a 
grindstone  when  turned,  of  a  swinging  pendulum,  or 
of  the  balance-wheel  of  a  watch,  are  called  mechanical, 
and  the  energy  they  represent  is  mechanical  energy ; 
while  the  motions  in  a  gas,  whether  of  one  kind  or 
another,  are  molecular,  and  the  energy  is  molecular 
energy.  Yet  it  should  be  borne  in  mind  that  this 
naming  is  only  for  convenience,  and  does  not  imply  or 
represent  any  fundamental  difference  in  matter  of 
different  sizes. 


MACHINES.  55 


QUESTIONS. 

1.  A  man  weighing  150  pounds  on  the  end  of  a  crowbar  5  feet 
from  the  fulcrum  is  just  sufficient  to  raise  a  stone  on  the  short 
end  of  the  bar  6  inches  from  the  fulcrum ;  what  is  the  weight  of 
the  stone  ? 

2.  In  what  ways  can  a  bar,  pole,  or  rod  be  used  to  do  work  ? 

3.  Can  a  rope  be  substituted  for  any  of  these  ? 

4.  What  is  the  difference  between  a  push  and  a  pull  ? 

5.  A  belt  is  transmitting  10  horse-power  to  a  pulley  5  feet  in 
diameter;  what  is  the  velocity  of  the  pulley? 

6.  If  an  air-molecule  be  moving  in  its  free  path  1500  feet  per 
second,  and  its  free  path  be  the  ^sTnnro  of  an  inch,  how  many 
times  does  it  strike  other  molecules  and  change  its  direction  in 
one  second  ? 

7.  The  crank  of  a  grindstone  is  one  foot  long.     If  it  requires 
a  constant  pressure  of  one  pound  to  rotate  the  stone,  how  many 
foot-pounds  of  work  are  done  in  one  revolution  ? 

8.  If  the  grindstone  be  3  feet  in  diameter,  what  pressure  upon 
its  face  will  be  needed  to  hold  it  still  if  the  push  upon  the  crank 
be  10  pounds  ? 


CHAPTER  VI. 

GASEOUS   PHENOMENA. 

The  Air.  —  The  atmosphere  that  surrounds  the  earth 
is  a  body  of  gas  which  is  held  to  the  earth  by  gravity  in 
the  same  way  that  other  bodies  are  held.  It  turns  round 
with  the  earth,  as  a  part  of  it.  At  the  equator  the  veloc- 
ity of  the  earth  is  more  than  a  thousand  miles  an  hour  ; 
at  the  poles  it  is  nothing.  Between  the  two  places  there 
is  a  constant  exchange,  which  gives  rise  to  extensive  air- 
currents  we  call  winds.  Because  the  air  has  mass,  the 
wind  results  in  pressure.  The  velocity  of  the  wind  is 
measured  by  a  machine  called  an  anemometer,  a  kind 
of  small  windmill,  and  its  pressure  varies  as  the  square 
of  its  velocity.  Wind-velocity  varies  within  wide 
limits  at  the  surface  of  the  earth,  from  no  wind  to 
tornado  velocities,  which  are  150  or  more  feet  per 
second.  This  wind-pressure  is  utilized  by  windmills 
for  purposes  where  a  slight  amount  of  power,  such  as 
pumping  water,  is  required.  Wind-pressure  at  mod- 
erate velocities  is  not  very  great,  being  for  one  mile  an 
hour  only  .005  of  a  pound  per  square  foot ;  but  as  its 
pressure  increases  as  the  square  of  the  velocity,  at  10 
miles  per  hour  it  will  be  .5  of  a  pound,  and  50  pounds 
at  100  miles  per  hour.  A  wind- wheel  25  feet  in  diam- 
eter, in  a  wind  blowing  15  miles  an  hour,  will  give  but 
about  one  horse-power. 


GASEOUS    PHENOMENA.  57 

Wind-pressure  is  the  result  of  a  current  or  a  body  of 
air  moving  in  some  given  direction,  and  is  thus  to  be 
distinguished  from  another  kind  of  pressure  in  the  air, 
which  is  due  to  the  individual  motions  of  its  molecules. 
The  latter  pressure  depends  upon  density  and  tempera- 
ture, and  exists  whether  the  wind  blows  or  not.  This 
is  called  gaseous  pressure. 

The  density  of  the  air  means  the  number  of  molecules 
per  cubic  inch ;  the  temperature  depends  upon  the  rate 
of  vibration  of  the  molecules,  which  gives  them  their 
translatory  motion.  There  are  so  many  molecules  in  a 
cubic  inch  that  each  one  can  move  but  a  short  distance 
before  it  bumps  against  another,  the  impact  changing 
the  direction  of  both.  The  distance  each  one  moves 
between  collisions  is  called  its  free  path.  The  dis- 
tances are  not  uniform,  but  the  average  of  the  distances 
is  called  the  average  free  path  of  the  molecule,  which, 
of  course,  depends  altogether  upon  the  density  of  the 
gas.  Each  molecule  of  air  or  of  any  gas  in  a  vessel  is 
free  to  move  in  any  direction,  and  is  moving  at  the 
rate  of  about  a  quarter  of  a  mile  per  second  ;  but  its 
path  is  short.  Some,  at  the  inner  surface  of  the  vessel, 
bump  upon  that  surface  and  press  outwards.  Many 
millions  per  second  do  this,  and  the  result  of  such  a 
bombardment  on  the  inner  surface  is  a  continuous 
outward  pressure  on  each  of  the  walls.  This  amounts 
ordinarily  to  nearly  15  pounds  per  square  inch  of  surface. 
Of  course  there  is  the  same  kind  of  action  and  pressure 
outside  as  inside  any  vessel,  and  so  there  is  equilibrium 
of  pressure,  as  illustrated  on  page  43  by  the  weight  on 
the  table.  If  we  contrive  to  extract  the  air  from  any 


58  NATURAL    PHILOSOPHY. 

inclosed  space  we  have  what  is  called  a  vacuum ;  but 
the  external  pressure  still  remains.  A  vacuum  may  be 
produced  by  a  machine  called  an  air-pump. 

It  consists  of  a  cylinder  B,  provided  with  a  movable 
piston  P  which  has  a  valve  s  in  it  opening  upwards. 
At  the  bottom  of  the  cylinder  is  another  valve  t  also 
opening  upwards.  A  tube  T  leads  from  the  cylinder  to 

a  flat  plate  L,  upon 
which  glass  jars  R, 
called  receivers,  may 
be  placed.  These  re- 
ceivers have  carefully 
ground  edges  so  as  to 
be  air  tight  when  in 
place. 

A    barometer    D    is 
sometimes  connected  to 

FIG.  12. 

the  tube  T  to  indicate 

the  degree  of  vacuum  produced.  When  the  handle  H 
is  pushed  down,  the  air  below  the  piston  is  com- 
pressed, valve  t  being  closed.  The  increased  pressure 
opens  s  and  allows  the  air  to  escape.  When  the  handle 
is  pulled  up,  the  valve  s  is  closed  and  the  air  in  the 
receiver  and  tube  opens  the  valve  at  t,  as  the  gaseous 
pressure  is  greater  below  the  valve  than  above  it. 
Each  upward  pull  removes  some  of  the  air  from  the 
receiver  into  the  cylinder  and  each  downward  push 
permits  the  escape  of  most  of  the  air  above  the  valve  t. 
With  an  ordinary  pump  of  this  kind  one  may  extract 
99  per  cent  of  the  air  from  a  receiver,  and  consequently 
leave  an  internal  pressure  in  it  of  only  -l-fa  of  a  pound 


GASEOUS    PHENOMENA. 


59 


per  square  inch.     With  such  a  machine  a  great  variety 
of  experiments  in  air-pressure  can  be  made. 

On  page  7  it  is  shown  what  an  enormous  number  of 
molecules  there  is  in  a  cubic  inch  of  matter  at  ordinary 
pressure.  If  the  gas-molecules  be  reduced  to  one- 
hundredth  of  their  num- 
ber, one  can  see  from  the 
figures  that  the  number  of 
molecules  will  not  be  ap- 
parently much  changed, — 
21,000000,000000,000000. 
Divide  it  by  a  million  and 
there  is  still  an  astonishing 
number  left.  Dividing  by 
a  million  will  reduce  the 
pressure  a  million  times; 
but  it  is  difficult  even  to 
approach  a  perfect  vacuum. 
By  the  most  perfect  means 
at  our  disposal  now,  it  is 
possible  to  reduce  the  pressure  to  the  hundred-millionth 
part  of  15  pounds  per  square  inch. 

The  pressure  of  the  air  may  be  "measured  by  pro- 
viding a  tube  32  or  33  inches  long,  filling  it  with 
mercury,  and  then  carefully  inverting  it  in  a  cup  of 
mercury  (Fig.  13),  not  allowing  any  air  to  enter  the 
tube.  The  air-pressure  will  then  be  able  to  balance  the 
pressure  of  a  column  of  mercury,  which  is  usually  about 
30  inches  high,  but  varies  from  that  an  inch  or  more 
either  way.  Such  a  machine  is  called  a  mercury  Ixi- 
.  and  it  lias  important  uses  in  the  study  of  tlie 


FIG.  13. 


60  NATURAL   PHILOSOPHY. 

weather.  We  may  find  what  the  pressure  of  the  air  is 
by  weighing  the  mercury  in  the  tube.  If  the  column 
of  mercury  be  a  square  inch  in  section,  and  30  inches 
high,  which  just  balances  the  pressure  of  the  air,  it  will 
equal  the  weight  of  30  cubic  inches  of  mercury,  which 
is  nearly  15  pounds. 

Another  kind  of  barometer,  called  the  aneroid  (Fig. 
14),  is  in  common  use.  It  consists  of  a  shallow 
metallic  box,  having  a  thick 
back  and  a  thin,  flexible  face. 
This  box  is  partially  exhausted 
of  air  and  then  hermetically 
sealed.  The  thin  face  moves 
in  and  out  as  the  air-pressure 
is  greater  or  less,  and  this  move- 
ment of  the  face  acts  upon  a 
mechanism  for  changing  the 
direction  of  motion,  and  for 
amplifying  it  by  a  hand  that 

moves  over  a  circular  scale,  where  its  movements  may 
be  observed. 

When  air  is.  condensed  by  forcing  it  to  occupy  less 
than  its  usual  volume,  it  is  found  that  its  pressure 
increases  as  its  density;  so  that  if  a  cubic  foot  at  15 
pounds  per  square  inch  pressure  be  reduced  to  half  a 
cubic  foot,  the  pressure  will  be  30  pounds  to  the  square 
inch.  If  it  be  ma$e  less  dense  by  giving  it  double 
the  space,  its  pressure  will  be  reduced  to  7£  pounds. 
and  so  on.  Thus  it  appears  that  the  density  of  a  <j<ix 
varies  inversely  as  the  volume  it  is  m<i<J<-  t<>  <><'(•>< />_!/.  This 
is  known  as  Boyles  Law.  That  its  pressure  should 


GASEOUS    PHENOMENA.  61 

vary  as  its  density  follows  from  the  fact  that  gaseous 
pressure  upon  a  surface  depends  upon  the  number  of 
molecules  that  strike  the  surface  at  a  given  instant, 
and  is  proportional  to  that  number. 

The  higher  one  climbs  a  mountain,  the  less  the 
number  of  molecules  in  the  air  per  cubic  inch,  and  con- 
sequently the  less  the  pressure ;  and  this  is  shown  by  the 
barometer.  If  one  observe  the  barometer  to  stand  at 
the  height  of  30  inches  at  the  sea-level,  and  then  carries 
it  up  on  a  hill,  mountain,  or  in  a  balloon,  he  will  see  that 
at  the  height  of  900  feet  the  mercury  will  have  fallen 
about  an  inch;  at  the  height  of  a  mile,  6  inches,  at 
the  height  of  3  miles,  nearly  15  inches.  Almost  half 
of  the  atmosphere  is  below  the  latter  elevation.  With 
a  good  barometer  one  may  easily  observe  the  difference 
in  pressure  between  the  ground  and  the  second  story  of 
a  house. 

Gaseous  Buoyancy.  —  A  hollow  metallic  globe  (Fig. 
15)  that,  whether  full  or  empty,  keeps  the  same  volume, 
weighs  less  when  the  air  has  been  removed  from  it  by  an 
amount  equal  to  the  weight  of  the  air 
displaced.  A  soap-bubble  blown  with 
common  gas  will  rise  rapidly  in  the 
air,  for  it  weighs  less  than  the  air  that 
it  displaces.  Suppose  the  bubble  to 
have  a  volume  of  100  cubic  inches,  — 
it  will  displace  31  grains  of  air.  If  the  j 
weight  of  the  bubble  and  its  contained 
air  be  20  grains  it  will  be  subject  to  an 
upward  pressure  of  31  —  20  =  11 


62  NATURAL   PHILOSOPHY. 

grains  ;  that  is,  the  difference  between  its  total  weight 
and  the  weight  of  the  air  displaced  by  it.  This  is  the 
principle  of  the  balloon.  Let  a  balloon  and  its  contents 
weigh  100  pounds,  and  its  volume  be  great  enough  to 
displace  300  pounds  of  air,  —  it  will  have  an  ascen- 
sional pressure  of  200  pounds,  and  can  easily  carry  up  a 
man  of  ordinary  weight. 


CHAPTER   VII. 
LIQUID   PRESSURE. 

THE  same  principles  that  apply  to  gases  apply 
equally  well  to  liquids.  The  weight  of  a  cubic  foot 
of  water  is  62.5  pounds;  consequently  this  is  the  weight 
that  must  be  supported  in  order  to  sustain  a  cube  of 
water  one  foot  square.  If  another  cube  be  put  on 
top  of  the  first,  the  pressure  on  the  bottom  will  be  62£ 
X  2  —  125  pounds.  The  pressure  is  proportional  to 
the  depth.  Hence  the  pressure  per  square  foot  for 
any  depth  is  equal  to  62J  multiplied  by  the  depth 
in  feet.  The  pressure  on  a  square  inch  is  the  y^? 

fi^  c 
of  what  it  is  for  a  square  foot :  -^-  =  .435  of  a  pound. 

If  a  tube  35  or  40  feet  long  be  filled  with  water,  as  the 
barometer  tube  was  with  mercury,  and  then  be  inverted 
in  a  tub  of  water,  the  water  will  stand  at  such  a  height 
in  it  as  will  give  a  pressure  of  1 5  pounds  per-  square 
inch,  the  pressure  of  the  atmosphere.  If  the  tube  be  one 
squai'e  inch  in  section,  then  the  pressure  of  one  foot  in 
length  will  be  .435  of  a  pound,  and  to  weigh  15  pounds 

the  column  must  be  — — -  =  34  feet  long ;    that  is,  a 
.4o5 

column  of  water  34  feet  long  balances  the  pressure  of 
the  atmosphere  on  a  square  inch. 

The  common  suction-pump  (Fig.  10)  utilizes  this 
pressure,  and  with  it  water  cannot  1x3  made  to  rise 


64 


NATURAL   PHILOSOPHY. 


higher  than  34  feet,  and  generally  not  so  high,  owing 
to   imperfections   in   the   joints   which  let   air  in  be- 
i]  tween  the  valve  and  the  top  of  the 

water  in  the  pipe.  The  higher  the 
hill  or  mountain  on  which  the  pump 
is  placed,  the  less  the  distance  to 
which  air-pressure  will  raise  water. 
The  denser  the  liquid  the  shorter  the 
distance  it  may  be  raised  in  this  way. 
If  some  mercury  be  poured  into  a 
glass  U-tube  (Fig.  17),  the  surface  of 
the  mercury  will  be  at  the  same 
height  in  both  branches.  If  water  be 
poured  into  one  of  the 
branches,  it  will  so  press 
upon  the  mercury  as  to  d 
lower  the  height  in  that 
branch  and  raise  it  cor- 
respondingly in  the  other. 
The  column  of  mercury 
ab  will  now  balance  the  column  of  water 
dc,  and  by  measuring  the  length  of  these 
columns  one  can  determine  how  many  times 
one  of  these  is  longer  than  the  other,  which  will  give 
their  difference  in  density.  The  column  of  water  will 
be  13.6  times  longer  than  that  of  the  mercury  column. 
The  density  of  mercury  is  13.6.  If  alcohol  were  used 
instead  of  water  its  column  would  be  longer,  for  alcohol 
is  less  dense. 

Specific  Gravity.  —  When  a  cup  is  placed  upon  the 
surface  of  water  it  floats.     It  has  displaced  some  of  the 


LIQUID    PRESSURE.  65 

water,  enough  to  balance  the  weight  of  the  cup.  If  the 
cup  be  pressed  still  deeper  it  will  displace  still  more 
water,  and  the  pressure  upwards  will  be  proportionally 
greater.  Whatever  be  the  weight  or  solidity  of  a  body 
which  is  submerged  in  water  it  will  displace  a  volume 
of  water  equal  to  its  own  volume,  and  will  be  pressed 
upwards  so  as  apparently  to  lose  as 
much  weight  as  is  equal  to  that  of  the 
displaced  water.  Thus,  if  a  body  dis- 
places a  pound  of  water  it  weighs  a 
pound  less  in  water  than  in  the  air. 
If  a  body  weighs  seven  pounds  in  the 
air,  and  only  six  in  the  water,  the  loss 
in  weight  is  one  pound.  The  ratio  of 
the  weight  of  a  body  in  air  and  its  loss 
in  water  is  called  the  specific  gravity  of  the  body. 
Let  w  be  the  weight  of  a  body  in  air  and  I  the  loss 

when  weighed  in  water  (Fig.  18),  then  —  =  specific  grav- 
ity.    There  is  a  distinction  between  the  specific  density 
of  a  body  and  its  specific  gravity,  for  specific  density 
_  density  of  the  body 
density  of  the  water 

.„  .,  weight  of  the  body 

and  specific  gravity  =  — — r-^-  —  • 

weight  of  an  equal  balk  ot  water 

But  the  two  ratios  are  numerically  equal,  so  that  the 
number  for  the  specific  gravity  of  a  body  is  the  same  as 
for  its  density. 

The  specific  gravity  of  a  liquid  is  its  weight  compared 
with  the  weight  of  an  equal  volume  of  water. 

The  specitie  gravity  of  a   liquid   may  be  determined 


66  NATURAL  PHILOSOPHY. 

by  carefully  weighing  a  vial,  filling  it  with  pure  water, 
and  weighing  it  again  to  find  the  weight  of  water  it  will 
contain.  Then  fill  it  with  the  liquid  to  be  determined, 
and  find  its  weight.  Dividing  the  weight  of  the  latter 
by  the  weight  of  the  water  will  give  the  specific  gravity 
of  the  liquid.  Thus,  if  the  vial  weighs  500  grains, 
filled  with  water,  850,  and  filled  with  alcohol,  780  grains, 
the  water  weighs  850  —  500  =  350  grains,  alcohol 

280 

780  —  500  =  280  grains,  and  -f-  =  .8  =  specific  grav- 

ooO 

ity  of  alcohol. 

Flotation.  —  A  piece  of  wood  will  float  on  water, 
and  to  make  it  sink  an  additional  weight  must  be 
applied.  A  piece  of  solid  iron  will  readily  sink  in 
water,  yet  a  tin  cup,  which  is  chiefly  made  of  iron,  will 
float,  and  the  largest  steam- 
ships, which  are  made  of 
iron,  will  float  safely  across 
the  ocean.  This  can  be 
understood  by  recalling  that 
when  a  body  is  placed  in 
water  it  displaces  some  of  the  water  and  is  pressed 
upwards  by  a  pressure  equal  to  the  weight  displaced. 
A  cubic  foot  of  iron  will  displace  a  cubic  foot  of  water, 
and  will  lose  62|  pounds  in  weight  when  immersed  ; 
but  if  the  iron  be  shaped  into  a  vessel  so  as  to  displace 
a  weight  of  water  equal  to  its  own  weight,  it  will  just 
float  (Fig.  19).  The  specific  gravity  of  iron  is  7.8,  and 
if  it  can  be  so  shaped  as  to  displace  7.8  cubic  feet  of 
water  it  will  float ;  and  if,  by  making  it  thinner  it  can 
be  made  still  more  capacious,  it  can  be  loaded  until  the 


LIQUID    PRESSURE.  67 

combined  weights  displace  an  equal  weight  of  water. 
The  weight  of  a  vessel  with  its  cargo  is  always  equal 
to  the  weight  of  water  which  it  displaces,  or  62 J  times 
the  number  of  cubic  feet  of  water  it  displaces.  A  cubic 
foot  of  gold  in  order  to  float  would  have  to  be  so  shaped 
as  to  displace  19  cubic  feet  of  water,  and  a  cubic  foot 
of  aluminum  2.6  cubic  feet. 

QUESTIONS. 

1.  If  the   pressure  of   the  wind  vary  as   the   square   of  its 
velocity,  what  will  be  its  pressure  at  50  miles  an  hour,  if  at  1  mile 
per  hour  it  be  .005  pound  ? 

2.  At  the  top  of  Mt.  Washington  the  wind  has  been  observed 
to  reach  the  velocity  of  150  miles  per  hour,  what  then  was  the 
pressure  per  square  foot  ? 

3.  What  is  the  pressure  upon  the  sails  of  a  windmill  with  100 
square  feet  of  sail  surface  when  the  wind  blows  10  miles  an  hour? 

4.  What  is  the  pressure  per  square  inch  in  water  at  the  depth 
of  5  feet? 

5.  If  a  cubic  foot  of  air  be  taken  when  the  pressure  is  15 
pounds  per  square  inch,  and  it  be  immersed  in  water  to  the  depth 
of  10  feet,  how  much  will  its  bulk  be  reduced? 

6.  A  brick  is  8  inches  long,  4  inches  wide,  and  2  inches  thick ; 
what  weight  of  water  will  it  displace  ? 

7.  A  cubic  foot  of  iron  is  so  shaped  that  it  just  floats  when 
placed  upon  water ;  what  volume  of  water  does  it  displace  ? 

8.  How  much  less  will  a  cubic  foot  of  iron  weigh  in  water  than 
in  air?     How  much  less  will  a  cubic  foot  of  gold  weigh  under 
.similar  conditions? 

9.  If  a  cubic  foot  of  marble  weigh  162  pounds,  what  will  be 
its  specific  gravity? 

10.  If  the  specific  gravity  of  silver  be  11,  what  will  be  the 
weight  of  one  cubic  foot  of  it? 

11.  What  will  a  gallon  (231  cubic  inches)  of  coal  oil  weigh  if 
its  specific  gravity  be  .9  ? 


CHAPTER   VIII. 

ON  HEAT. 

LET  the  hand  be  placed  in  contact  with  any  object, 
as  a  book,  a  pencil,  or  a  table.  By  the  sense  of  touch 
we  become  conscious  of  the  contact,  and  by  moving  the 
fingers  upon  it  the  same  sense  of  touch  informs  us 
whether  the  surface  is  plane,  curved,  or  angular,  smooth 
or  rough,  so  that  even  witn  the  eyes  closed  we  may 
determine  the  form  of  a  body  if  it  can  be  touched.  If 
a  piece  of  ice  be  touched,  in  addition  to  the  sensation 
of  contact  of  form  and  the  character  of  the  surface,  a 
different  sensation  is  perceived,  which  we  call  coldness. 
On  the  other  hand,  if  a  poker  that  has  been  a  little 
while  in  glowing  coals  be  touched,  in  addition  to  the 
sensation  of  contact  there  will  be  another  sensation, 
which  we  call  hotness,  -of  which  there  are  all  degrees, 
so  that  we  speak  of  hot  bodies  and  cold  bodies,  and 
their  difference  in  this  respect  we  call  their  difference 
in  temperature.  Such  terms  as  warm  and  cool  are 
generally  employed  to  denote  temperatures  that  are 
agreeable.  Such  expressions  as  "a  warm  day,"  "a  cool 
breeze"  imply  temperatures  that  are  not  unpleasant, 
while  "a  hot  day"  and  "a  cold  wind"  imply  discomfort. 
In  this  way  by  our  feelings  we  judge  temperature.  The 
sense  of  temperature,  which  all  possess,  does  not  tell  us 
of  the  amount  of  the  difference  in  temperature.  If  one 
should  ask  how  much  hotter  a  hot  day  is  than  a  warm 


ON    HEAT.  69 

or  a  cool  one,  only  some  vague  and  indefinite  answer 
could  be  given.  We  need  to  depend  upon  other  senses 
than  feeling  to  answer.  Physiologists  tell  us  that  we 
have  a  particular  set  of  nerves  in  the  body,  the  function 
of  which  is  to  perceive  heat,  as  we  have  nerves  for  the 
perception  of  touch,  taste,  and  sight.  A  particular  set 
of  nerves  implies  a  particular  agency  capable  of  acting 
upon  them,  and  the  agency  for  this  set  of  nerves  is 
called  he'at,  but  the  phenomena  of  heat  are  apparently 
so  unlike  the  phenomena  of  such  mechanical  bodies  as 
we  can  see,  and  which  have  been  considered  in  the 
previous  chapters,  that  they  form  a  separate  part  of 
physics,  and  introduce  laws  that  will  be  new  to  the 
student. 

THE   ORIGIN   OF   HEAT. 

I.  Friction.  —  If  one  will  rub  his  knuckles  briskly 
upon  his  coat  sleeve,  he  will  find  presently  the  heat 
sensation  unbearable.  A  metalic  button,  rubbed  in  the 
same  way  on  the  floor  gets  too  hot  to  hold  with  comfort 
in  the  fingers.  Such  mechanical  action  as  this  we  call 
friction,  and  it  has  been  found  that  wherever  there  is 
friction  heat  is  generated.  The  friction  brake  on  cars 
to  bring  them  quickly  to  rest  is  a  good  example  of  this, 
for  the  brake  when  applied  may  be  seen  in  the  night  to 
be  giving  a  shower  of  sparks,  and  if  touched  after  the 
cars  have  stopped  may  be  found  hot.  In  the  absence  of 
a  supply  of  lubricating  oil  the  friction  on  the  car  axles 
sometimes  sets  afire  the  waste  in  the  boxes.  Count 
Rumford  found  that  water  could  be  made  to  boil 
by  the  heat  generated  by  boring  a  cannon ;  and  Sir 


70  NATURAL   PHILOSOPHY. 

Humphry  Davy  was  able  to  melt  two  pieces  of  ice  by 
rubbing  them  together.  The  scratching  of  a  common 
match  heats  the  end  till  it  takes  fire. 

II.  Impact.  —  A  blacksmith   may  hammer  a  small 
piece  of  iron  until  it  is  too  hot  to  hold.     A  bullet  that 
has  just  struck  the  target  is  hot,  and  in  the  dark  may 
be  seen  to  produce  a  flash  at  the  instant  of  impact. 

III.  Chemism.  —  When  coal,  wood,  or  any  combus- 
tible thing  is   burned,  there   is  much  heat  produced. 
This  is  a  chemical  phenomenon,  and  is  due  to  chemical 
combination  going  on  at  a  rapid  rate.     Also,  if  a  test 
tube  be  filled  to  the  depth  of  an  inch  with  water,  and  an 
equal  volume  of  strong  sulphuric  acid  be  then  poured 
into  it,  the  mixture  will  become  too  hot  to  hold.    There 
is  chemical  action  here,  and  if  care  be  taken  to  observe 
accurately  the  volumes  of  the  two  liquids  used,  it  will 
be  found  when  the  mixture  has  cooled  that  the  result- 
ing volume  will  not  be  equal  to  the  sum  of  the  volumes 
used. 

IV.  Electricity.  —  An  electric  current  may  produce 
a  very  high  degree  of  heat.     The  electric  light  itself  is 
due  to  the  hot  carbons,  which  shine. 

In  each  of  these  cases  it  is  to  be  observed  that  what 
immediately  proceeds  the  appearance  of  heat  is  some 
kind  of  energy  that  is  spent  in  producing  the  heat. 

In  the  case  of  friction,  the  train  of  cars  has  a  trans- 
latory  mechanical  motion,  which  the  friction  of  the 
brakes  stops,  and  in  place  of  the  mechanical  motion 
heat  appears.  When  the  stroke  of  the  hammer  falls 


ON    HEAT.  71 

upon  the  nail,  or  the  bullet  strikes  the  target,  there  is 
the  same  translatory  motion  of  a  relatively  large  mass 
of  matter  suddenly  stopped,  the  heat  appearing  as  its 
substitute. 

In  like  manner  when  air  is  suddenly  compressed,  as 
in  the  condensing  syringe  (Fig.  20),  the  heat  resulting 
is  so  great  as  to  ignite  a  piece  of  punk  fixed  at  the  end 
of  the  piston.  This  means  that  the  relatively  long  free 


3=) 


FIG.  20. 

paths  of  the  molecules  of  the  air  are  suddenly  reduced, 
the  molecules  strike  each  other  more  frequently,  and  a 
flash  may  be  seen  if  it  be  done  in  the  dark. 

When  coal  is  burned  its  atoms  combine  with  oxygen 
of  the  air,  and  there  are  violent  atomic  collisions  pro- 
ducing a  continuous  flash,  which  we  call  a  flame  or 
glow ;  and  when  an  incandescent  lamp  filament  is  made 
red-hot  by  the  electric  current,  the  steam-engine  or 
water-wheel  is  spending  its  energy  of  mechanical 
motion  to  maintain  it.  Mechanical  motions  of  large  or 
small  bodies  are  the  antecedents  of  heat  in  every  case. 
We  have  already  considered  how  one  kind  of  motion  is 
capable  of  being  changed  into  some  other  kind,  also 
that  such  changes  are  not  limited  to  large  masses  of 
matter,  but  are  equally  possible  to  the  smallest.  Impact 
upon  a  tuning-fork  makes  the  latter  vibrate  on  account 
of  its  elasticity.  There  are  the  best  of  reasons  for 
believing  that  atoms  and  molecules  are  elastic  bodies, 
and  when  struck  in  any  way  must  vibrate  like  other 


72  NATURAL   PHILOSOPHY. 

Elastic  bodies,  and  must  also  have  some  rate  of  vibration 
peculiar  to  each  element.  This  may  be  made  clear  to 
mechanically  minded  persons  by  considering  what  must 
happen  to  an  elastic  ring  (Fig.  21)  when  its  sides  arc 
pulled  out  and  then  let  free.  It  will  swing  backwards 
and  forwards  first  to  a  vertical  ellipse,  then  to  a  hori- 
zontal ellipse,  and  so  on.  A  ring 
six  or  eight  inches  in  diameter, 
made  of  brass  or  steel  wire,  will 
show  this  kind  of  motion,  which 
is  vibratory  as  the  result  of  me- 
chanical impact.  This  is  the 
kind  of  motion  among  atoms 
and  molecules  which  one  is  to 

FIG.  21.  ,  .     ,  .,      . 

keep    in    mind   as    that   set    up 

among  them  when  energy  of  any  kind  is  spent  upon 
them  so  as  to  produce  heat.  It  is  like  the  trembling 
motion  of  a  bell  when  it  is  struck.  Heat  is  this 
vibratory  motion  of  atoms  and  molecules  when  hot. 
They  do  not  necessarily  have  any  translatory  or  oscil- 
latory motion. 

TEMPERATURE  AND   ITS   MEASURE. 

Our  sensations  of  heat  are  not  acute  enough  to 
enable  us  to  determine  by  the  feeling  how  much  hotter 
one  body  is  than  another  with  any  degree  of  precision. 
How  little  one's  feelings  can  be  relied  upon  may  be 
learned  by  such  experiments  as  the  following.  Fill  two 
basins  with  water  of  the  same  temperature,  and  place 
one  hand  in  each;  to  one  hand  it  may  seem  warmer 


ON   HEAT.  73 

than  to  the  other.  Again,  having  three  basins,  —  one 
holding  water  as  hot  as  can  be  borne,  the  second, 
water  ice-cold,  the  third,  an  equal  mixture  of  the  hot 
and  the  cold,  —  place  one  hand  in  the  hot  water,  the 
other  in  the  ice-cold,  and  let  them  stay  a  few  seconds. 
Then  dip  both  hands  into  the  third  basin  ;  the  hand  that 
was  in  the  hot  water  will  feel  very  cold,  while  the  hand 
that  has  been  in  the  cold  water  will  feel  hot.  In  some 
fevers  one  may  feel  very  chilly  when  he  is  really 
several  degrees  warmer  than  the  natural  temperature 
of  the  body.  If,  then,  we  are  to  measure  differences  in 
the  warmth  of  bodies,  we  must  depend  upon  something 
else  than  sensation.  In  reality  we  employ  its  mechan- 
ical effects,  —  its  expansive  power  on  either  solids,  or 
liquids,  or  gases.  An  instrument  measuring  this  power 
is  called  a  thermometer  (a  measure  for  temperature).  The 
common  form  with  which  all  are  familiar  consists  of  a 
glass  bulb  on  the  end  of  a  long  tube.  Mercury  fills  the 
bulb  and  reaches  a  short  distance  into  the  stem  at  the 
lowest  degree  of  cold  to  which  it  will  be  subjected. 
If  this  bulb  be  thrust  into  ice-cold  water,  the  end  of  the 
mercury  column  will  reach  a  certain  point  on  the  tube, 
which  may  be  marked  upon  it ;  or,  as  is  more  commonly 
done,  a  scale  plate  may  be  firmly  attached  to  the  stem 
and  the  height  of  the  mercury  column  be  scratched 
upon  it.  If  the  whole  be  thrust  into  boiling  water, 
the  mercury  will  expand  and  fill  the  tube  to  a  higher 
level ;  and  if  this  place  be  marked  on  the  scale,  there 
will  be  the  two  fixed  points  indicating  the  freezing 
and  boiling  points  of  water.  These  are  found  to  be 
uniform,  and  the  mercury  will  move  to  these  points 


74 


NATURAL    PHILOSOPHY. 


100- 


—213° 


respectively  when  placed  in  freezing  or  in  boiling 
water.  The  space  on  the  scale  between  these  two  fixed 
points  is  graduated  in  two  different  ways.  In  one,  F 
(Fig.  22),  the  space  is  divided  into  180  equal  parts 
called  degrees,  and  the  lowest  one  is  marked  32.  The 
same  spacing  is  carried  still  further  down  the  scale,  to 
c  F  0  or  below,  where  the  numbers  begin  1, 
2,  3,  and  so  on,  and  are  read  below  zero. 
This  makes  the  difference  between  0  and 
the  boiling  point  of  water  to  be  212  such 
divisions  or  degrees.  Such  a  scale  is 
called  Fahrenheit  Scale.  In  the  other 
way,  C  (Fig.  22),  the  space  between  the 
freezing  and  boiling  points  of  water  is 
divided  into  100  equal  parts  called  de- 
grees, the  freezing  point  of  water  being 
the  zero  of  this  scale.  This  is  a  very 
convenient  scale  for  scientific  work,  and 
is  -called  the  Centigrade  ;  but  the  other 
is  in  most  common  use,  and  will  be  em- 
ployed in  this  book.  With  either  of  these 
thermometers  it  is  possible  to  find  the 
degree  of  heat  in  the  air,  in  liquids,  or  in  other  bodies. 
Their  scales  are  convertible  from  one  to  the  other,  for 
180  divisions  of  the  Fahrenheit  are  equal  to  100  of  the 
Centigrade,  ^--|^  =  |.  That  is,  one  degree  Centigrade 
is  |  larger  than  the  Fahrenheit ;  but  their  zeros  do  not 
coincide  ;  therefore  to  reduce  Fahrenheit  degrees  to 
Centigrade  degrees,  subtract  32  and  multiply  by  |. 
To  reduce  Centigrade  degrees  to  Fahrenheit,  multiply 
by  %  and  add  32.  For  example :  A  Fahrenheit  ther- 


17.75- 


GO 

FIG.  22. 


(>N     HEAT.  75 

mometer  indicates  80° ;   what  would  be  the  indication 
on  a  Centigrade  thermometer? 

80  —  32  =  48,  48  X  |  =  26.6°  C. 

What  is  the  reading  on  a  Fahrenheit  scale  when  the 
Centigrade  reads  25°  ? 

25  X  |  =,  45  45  +  32  =  77°  F. 

Sometimes  thermometers  are  filled  with  alcohol  in- 
stead of  mercury,  as  it  will  not  freeze  at  the  tempera- 
ture that  will  solidify  the  metal,  but  the  scales  are 
constructed  in  the  same  way.  The  following  table 
gives  some  of  the  temperature  ranges  to  be  met  with: 

ABOVE  0°  F. 

Electric  arc 6000° 

Platinum  melts 3400° 

Bright  red  heat          ......  1200° 

Red  heat  just  visible 1000° 

Heat  observed  in  India 140° 

Human  body 98.6° 

Water  freezes 32° 

Mixture  of  ice  and  sal  ammoniac  ...  0° 

BELOW  0°  F. 

Mercury  freezes —  39° 

Arctic  cold —  70° 

Artificial  cold —400° 

Absolute  cold —459° 

Temperature  of  space — 459° 

Excepting  the  last  two,  these  are  observed  tempera- 
tures.     The  last  figure  is  called  absolute  zero  to  dis- 


76  NATURAL   PHILOSOPHY. 

tinguish  it  from  the  other  zeros.  It  is  believed  to  be 
correct,  for  reasons  that  will  be  given  further  along 
in  the  book. 

THERMODYNAMICS. 

The  temperature  of  a  cupful  of  water  would  evi- 
dently be  the  same  as  that  of  the  remaining  water  in 
the  pail  from  which  it  was  taken,  but  the  amount  of 
heat  would  depend  upon  the  quantity  of  water ;  in  two 
cups  full  there  would  be  twice  as  much  as  in  one.  The 
temperature  of  a  spark  might  be  a  thousand  degrees, 
but  it  would  not  have  heat  enough  to  make  an  appre- 
ciable difference  in  the  temperature  of  a  pail  of  water 
if  quenched  in  it.  It  is  plain,  then,  that  a  distinction 
must  be  kept  in  mind  between  the  temperature  a  body 
may  have  and  the  amount  of  heat  it  may  have.  Seeing 
that  it  will  take  twice  as  much  heat  to  heat  two  pounds 
of  water  one  degree  as  it  will  to  heat  one  pound  one 
degree,  it  has  been  found  convenient  to  adopt  a  heat 
unit,  which  is  the  amount  of  heat  necessary  to  raise  the 
temperature  of  a  pound  of  water  one  degree.  When  ten 
pounds  of  water  are  heated  ten  degrees,  the  water  is 
said  to  possess  100  heat  units,  and  if  heated  100°, 
1000  heat  units.  When  a  pound  of  water  at  boiling 
point,  212°,  is  cooled  in  any  way  to  freezing  point,  32°, 
it  has  lost  180  heat  units. 

It  has  been  pointed  out  that  friction  results  in  heat, 
and  if  water  be  subject  to  friction  it  becomes  heated. 
Churning  it  by  revolving  a  paddle  in  it  heats  it  appre- 
ciably. By  arranging  a  paddle  p  (Fig.  23)  in  a  known 
weight  of  water  in  B,  and  driving  the  paddle  by  means 


ON    HEAT. 


77 


of  a  known  weight  W  falling  a  given  distance,  one  may 
know  how  much  work  is  being  done  by  multiplying 
the  weight  by  the  distance  it  falls ;  and  by  noting  the 
temperature  of  the  water  at  the  beginning  and  at  the 
end  of  the  operation  by  the  thermometer  t,  the  rise  in 
temperature  equivalent  to  the  work  is  known.  Careful 
experiments  of  this  kind  have  shown  that  the  work 


done  by  778  pounds  falling  one  foot,  equal  to  778  foot- 
pounds, will  raise  the  temperature  of  one  pound  of 
water  one  degree.  As  the  amount  of  heat  necessary  to 
raise  a  pound  of  water  one  degree  is  the  heat  unit,  it 
follows  that  778  foot-pouwh  is  the  mechanical  equivalent 
of  one  heat  unit  —  a  number  to  be  remembered. 

This  means  that  the  energy  in  a  pound  of  water 
represented  by  one  degree  is  equal  to  the  energy  repre- 
sented by  778  foot-pounds,  and  if  that  water  energy 
be  properly  applied  it  is  capable  of  doing  that  amount 
of  work. 

Mechanical   energy  and    heat  energy  are    therefore 


78  NATURAL   PHILOSOPHY. 

convertible  quantities,  that  is,  either  may  be  changed 
into  the  other.  This  relation  may  be  thus  stated : 

Work  =  778  X  heat  units  ; 

which  is  called  the  first  law  of  thermodynamics.  For 
instance,  a  hundred  pounds  of  boiling  water  cools  to 
60°;  how  much  work  is  represented  by  the  loss  in 
temperature  ? 

212  —  60  =  152°  =  loss  in  temperature, 
152  X  100  =  15,200  total  loss  of  heat  units, 
15,200  X  778  =  11,825,600  foot-pounds. 

To  what  temperature  would  100  pounds  of  water  be 
raised  by  impact  on  the  earth  after  falling  a  mile  in  a 
vacuum  ? 

5280  X  100  =  528,000  foot-pounds, 

778  X  100  =  77,800  =  amount  of  work  needed  to 

raise  it  1°, 

^n¥rnr  —  6.8°  =  rise  in  temperature  due  to  the  fall. 
If  the  water  were  at  32°  to  begin  with,  its  tempera- 
ture after  the  striking  would  be  32  -f  6.8  =  38.8°,  if  all 
the  work  was  spent  on  it. 

FUELS. 

We  use  wood,  coal,  coal  oil,  and  gas  for  the  sake  of 
the  heat  that  can  be  got  from  them  when  allowed  to 
burn.  When  used  for  such  a  purpose  they  are  called 
fuels.  It  has  been  found  experimentally  that  the  heat- 
ing power  of  a  given  kind  of  fuel  depends  upon  its 
amount,  that  is,  its  weight.  When  a  pound  of  coal  is 
burned  in  the  air,  it  yields  a  product  of  carbonic  acid 


ON   HEAT.  79 

gas,  and  generates  heat  enough  to  raise  14,500  pounds 
of  water  1°,  —  that  is,  its  heating  power  is  14,500  heat 
units.  In  like  manner  the  heating  value  of  a  pound  of 
the  following  substances  has  been  determined : 

Wood 7,000  heat  units. 

Wax 19,000 

Phosphorus"     .  .  10,350         " 

Coal  gas 22,500 

Hydrogen 62,000 

Fats 17,460 

Coal  oil 18,000 

Bituminous  coal  .         .         .  14,700         " 

Anthracite 10,800 

Pure  carbon          ....  14,500         « 

These  numbers  are  to  be  understood  as  representing 
the  number  of  pounds  of  water  that  may  be  heated  one 
degree  by  the  combustion  of  one  pound  of  the  substance. 
For  instance,  a  pound  of  wood  when  burned  will  heat 
7000  pounds  of  water  one  degree  ;  a  pound  of  hydrogen 
will  heat  62,000  pounds  of  water  one  degree ;  and  so  on 
for  all  the  others.  It  should  be  remembered,  too,  that 
if  a  pound  of  wood  will  heat  7000  pounds  of  water  one 
degree,  it  will  heat  1000  pounds  7  degrees,  or  100 
pounds  70  degrees,  for,  the  product  of  the  weight  of 
water  into  its  rise  in  temperature  gives  the  heat  units. 

One  may  now  compute  how  much  working  power 
there  is  in  a  pound,  or  any  other  quantity,  of  any  sub- 
stance used  for  fuel  when  its  heat  unit  value  is  known. 
Tims,  the  mechanical  equivalent  or  working  power  of 
one  heat  unit  being  778  foot-pounds,  the  foot-pounds 
of  work  a  pound  of  wood  when  burned  can  do  is  equal 


80  NATURAL   PHILOSOPHY. 

to  the  product  of  the  mechanical  equivalent,  778,  mul- 
tiplied by  7000,  the  heat  unit  value  of  wood. 

778  X  7000  =  5,446,000  foot-pounds. 

For  bituminous  coal  it  is 

778  X  14,700  =  11,436,600  foot-pounds. 

Ten  or  a  hundred  pounds  of  either  will  of  course 
give  ten  or  a  hundred  times  the  amount  of  work  one 
pound  will  give. 

These  constant  numerical  relations  between  heat  and 
work  have  been  verified  in  many  ways,  and  now  when 
one  looks  on  a  lump  of  coal  he  may  be  able  to  see 
something  more  than  a  mere  lump  of  inert  matter.  Let 
him  compute  to  what  height  the  energy  in  the  lump  of 
coal  would  raise  it  if  it  were  applied  to  such  a  purpose. 
In  the  table,  fat  is  shown  as  having  more  energy  to  the 
pound  than  coal.  Fat  is  one  of  the  necessary  ingredi- 
ents of  food.  Indeed,  nearly  all  foods  may  be  used  as 
fuel,  and  each  particular  kind  has  its  own  heating 
value.  Bread  and  butter,  if  fed  into  a  furnace,  will 
make  steam  even  better  than  coal;  it  is  too  costly  for 
such  purpose  generally,  but  in  regions  where  wood  and 
coal  have  been  scarce,  corn  has  been  used  as  a  sul>- 
stitute.  One  may  consider  fuels  as  matter  laden  with 
a  definite  amount  of  chemical  energy  per  pound,  and 
such  as  are  used  for  foods  supply  the  body  with  the 
energy  needful  for  movements  and  for  its  various  func- 
tions. 

Bearing  this  in  mind,  if  one  can  know  the  heating 
value  of  the  food  he  eats  in  a  day,  he  may  compute 
approximately  the  amount  of  work  lie  can  do  in  the 


ON   HEAT.  81 

way  of  climbing,  shovelling,  and  so  forth.  When  one 
becomes  tired  he  has  nearly  used  up  his  supply  of 
energy,  and  as  the  bodily  organs  have  a  definite  rate  at 
which  they  can  transform  such  food  energy  into  work, 
they  can  be  made  to  work  but  at  a  definite  rate.  This  is 
very  different  with  different  individuals,  and  different 
races  of  men  have  very  different  natural  rates  of  such 
bodily  changes,  which  cannot  be  much  increased  by 
exercise. 

The  sources  of  heat  are  friction,  condensation,  per- 
cussion, chemical  action,  and  all  other  forms  of  energy, 
and  whenever  heat  appears,  some  other  kind  of  energy 
has  been  spent  to  produce  it.  The  amount  spent  is 
equal  to  that  of  the  heat  energy  produced.  We  have 

already  seen  that  energy  — —  and  work  pd  are  quan- 
titatively related,  and  here  we  have  a  similar  relation 
between  heat  and  work.  It  is  apparent  that  energy 
and  heat  are  directly  related  when  a  definite  amount  of 
one  is  convertible  into  a  definite  amount  of  the  other. 
Indeed,  we  shall  presently  see  that  it  is  only  a  trans- 
formation of  the  kind  of  motion  we  call  mechanical  or 
chemical  into  that  vibratory  kind  among  atoms  and 
molecules  that  we  call  heat. 

PHENOMENA   OF   HEAT. 

I.  Expansion.  —  1.  Solids.  It  is  a  familiar  enough 
fact  that  heat  expands  bodies,  and  the  action  in  ther- 
mometers illustrates  it,  whether  the  thermometers  be 
iniule  in  one  way  or  another.  It  remains  to  point  out 
how  it  is  that  heat-expands.  Consider  a  piece  of  wire 


82  NATURAL   PHILOSOPHY. 

an  inch  long,  made  of  any  substance.  Its  molecules 
are  in  the  neighborhood  of  the  fifty-millionth  of  an 
inch  in  diameter,  and  so  fifty  millions  in  a  row  make 
an  inch.  As  the  wire  is  a  solid  it  possesses  cohesion  — 
the  molecules  stick  tight  together.  Suppose  these 
molecules  be  absolutely  quiet,  having  no  motion  at  all, 
and  that  they  be  crowded  together  so  each  one  touches 
its  neighbor  like  a  row  of 

QQQQQQQQQQ  coins  or  rings  (Fig.  24).  In 
such  an  arrangement  the  dist- 
ance ab  (Fig.  24)  will  be  the 

shortest  length  into  which  this  row  may  be  crowded. 
Suppose,  however,  that  each  molecule,  by  vibratory 
motion,  changes  its  form,  elongating  and  contracting 
on  its  axis ;  each  one  will  then  need  more  room 
for  itself  than  it  needed  when  at  rest,  and  this  will 
result  in  elongating  the  row 

a! 1  b      (Fig.  25),    and  the  measure 

°°°  ab  will  be  too  short,— how 

•pwft      oe 

much  too  short  will  depend 

upon  how  great  may  be  the  amplitude  of  the  individual 
vibrations  multiplied  by  the  number  of  molecules  in  the 
length  measured.  If  the  amplitude  of  such  motion 
could  be  as  great  as  half  the  diameter  of  each  molecule, 
the  increase  in  the  length  would  be  half  the  original 
length,  and  the  inch  of  wire  would  become  an  inch  and 
a  half  long.  No  such  great  change  in  length  takes 
place  in  bodies,  so  no  such  relative  amount  of  motion  can 
take  place  in  a  single  molecule ;  but  if  one  can  measure 
the  increase  in  length  of  a  piece  of  wire  when  heated, 
he  can  determine  how  much  each  .molecule  moves  by 


ON    HEAT.  83 

dividing  the  increase  in  length  by  the  number  of  mole- 
cules in  the  length.  In  any  case  it  is  a  very  minute 
quantity,  measurable  in  terms  of  the  billionths  of  an 
inch,  and  in  thousandths  of  the  diameter  of  the  atom. 

The  increase  in  length  for  many  substances,  due  to  a 
rise  in  temperature  of  one  degree,  has  been  most  care- 
fully measured,  and  is  found  to  differ  very  much 
among  different  substances,  but  to  be  uniform  for  a 
given  substance.  The  rate  of  increase  for  a  unit 
length  for  one  degree  is  called  the  coefficient  of  linear 
expansion  of  a  substance. 

If  we  call  this  increase  in  length  for  one  foot  for  one 
degree  a,  then  I  feet  will  increase  la  for  one  degree, 
and  for  t  degrees  it  will  be  lat;  that  is,  the  increase  in 
length  will  be  proportional  to  the  length  of  the  bar  and 
to  the  temperature  to  which  it  is  raised.  Thus,  the 
coefficient  of  expansion  of  wrought  iron  is  .00000675, 
which  means  that  a  wrought  iron  rod  one  foot  long, 
when  heated  one  degree,  becomes  1.00000675  feet  in 
length;  if  one  mile  long  it  would  become  1.00000675 
miles,  the  increase  being  .0356  of  a  foot ;  if  heated  40° 
the  increase  would  be  40  times  that,  or  1.42  feet. 

The  following  table  gives  the  coefficient  of  linear 
expansion  for  some  of  the  common  substances : 

Glass 0000047 

Cast  iron 0000062 

Steel  hardened 0000068 

Steel  soft 0000060 

Copper 0000095 

Silver 0000105 

Lead     .    > 0000155 

Zinc  .0000163 


84  NATUKAL   PHILOSOPHY. 

Although  all  these  numbers  are  very  small,  it  may  be 
noticed  that  they  differ  a  good  deal,  some  of  them 
being  two  or  three  times  greater  than  others,  zinc 
having  the  greatest  expansion  rate. 

The  changes  in  length  due  to  difference  in  tempera- 
ture, while  small  for  small  bodies  and  for  ordinary 
variations  in  temperature,  become  noticeable  when 
either  one  is  considerable.  It  would  not  be  safe  to  lay 
railroad  rails  in  coldest  winter  weather  with  their  ends 
touching,  for  on  some  days  in  summer  the  temperature 
might  be  nearly  a  hundred  degrees  higher  and  the  rails 
would  be  correspondingly  longer,  a  difference  of  over 
three  feet  per  mile,  and  in  expanding  they  would 
crowd  each  other  out  of  place  and  endanger  travel. 
Tires  for  carriage  wheels  are  heated  four  or  five  hun- 
dred degrees  to  expand  them,  then  when  placed  in 
cooling  they  shrink  and  become  very  tight.  A  differ- 
ence of  the  hundredth  of  an  inch  in  the  length  of  a 
common  pendulum  causes  the  clock  to  err  about  ten 
seconds  in  twenty-four  hours,  and  a  rise  in  temperature 
of  25°  may  produce  this  difference.  To  counteract  this 
difference  a  glass  cylinder  filled  with  mercury  is  sub- 
stituted for  the  ordinary  disk.  As  the  rod  expands 
downwards  the  mercury  expands  upwards,  and  keeps 
the  center  of  gravity  at  the  same  distance  from  the 
point  of  support.  If  two  long  strips  of  metals  like  iron 
and  zinc  be  soldered  together  through  their  length, 
the  strip  will  curve  when  heated  or  cooled,  and  ther- 
mometers are  made  on  this  principle. 


ON    HEAT. 


85 


CUBIC   EXPANSION. 

Bodies  expand  in  breadth  and  thickness  as  well  as 
in  length  ;  and  in  general,  equally  in  all  directions. 
The  coefficient  of  volume,  or  cubic  expansion  as  it  is 
called,  is  ordinarily  three  times  what  it  is  for  the  linear 
expansion  ;  thus  for  copper  the  cubical  expansion  is 
.000001)5  X  3  =  .0000285.  Some  crystals  expand  un- 
equally in  their  different  dimensions ;  wood  also  expands 
and  contracts  more  in  breadth  than  in  length.  So  long 
as  there  is  no  chemical  change  produced  by  heating  or 
cooling,  all  bodies  regain  their  original  dimensions 
when  brought  to  their  original  temperatures.  This 
shows  that  the  changes  take  place  according  to  laws, 
and  one  may  rely  upon  uniformity  of  action  in  this  as 
in  all  other  physical  processes  in  nature. 

2.  Liquids.  Like  solids  liquids  change  their  volume 
when  their  temperatures 
change,  only,  on  account 
of  the  slighter  degree  of 
cohesion  among  their  mole- 
cules, their  change  in  vol- 
ume is  considerably  greater. 
Fill  a  glass  flask  (Fig.  26), 
holding  a  pint  or  more,  with 
water,  and,  having  a  glass 
tube  with  a  fine  bore  thrust 
through  the  cork  ;  stop  it 

FIG.  'J6. 

tight  and  so  that  the  liquid 

stands  at  some  height  in  the  tube ;  tie  a  thread  around 

the  tube  to  mark  the  place  of  the  top  of  the  water.    The 


86  NATURAL   PHILOSOPHY. 

warmth  of  the  hands  on  the  flask  will  be  sufficient  in  a 
few  seconds  to  make  an  appreciable  rise  in  the  tube. 
The  same  is  true  of  mercury.  There  is  a  curious  ex- 
ception to  the  increase  of  volume  on  heating  observable 
water.  If  water  at  the  freezing  point,  32°,  be  taken  in 
for  the  above  experiment,  the  volume  will  decrease  and 
the  top  of  the  column  in  the  tube  will  fall  until  the 
temperature  rises  to  39°,  when  it  will  begin  to  increase 
again.  In  this  way  it  has  been  found  that  water  is  at 
its  greatest  density  at  39.2°.  Water  at  this  temperature 
expands,  whether  it  be  heated  or  cooled.  The  cubical 
expansion  of  mercury  and  of  alcohol  are  utilized  in 
the  making  of  thermometers,,  the  cubical  expansion  of 
mercury  being  .00010  per  degr.ee,  and  of  alcohol  .00055. 
3.  Gases.  As  gases  consist  of  molecules  that  do  not 
cohere,  but  freely  move  about  and  bump  against  each 
other,  it  may  be  expected  that  the  effect  of  Ideating  the 
molecules  will  be  to  make  them  move  more  quickly, 
bump  harder,  and  require  more  room  for  each  molecule ; 
so,  if  there  be  room,  a  volume  of  heated  gas  will  beat 
back  the  neighboring  gas  and  occupy  more  space,  — 
that  is,  it  will  expand,  and  for  a  given  degree  of  rise  in 
temperature  will  expand  very  much  more  than  any 
solid  or  liquid,  for  it  has  no  molecular  cohesions  to 
counteract.  If  a  given  volume  of  air  or  other  gas  be 
taken  at  32°  and  raised  one  degree  in  temperature,  it  is 
found  that  its  volume  has  increased  ^y  part.  If  it  be 
heated  two  degrees  its  volume  has  increased  ^| j ;  and 

so  on  for  any  number  of  degrees,  being  always  -— -,  so 

4y -L 

if  it  be  raised  491°  its  volume  will  be  doubled. 


ON    HEAT.  87 

In  like  manner,  if  the  same  volume  at  32°  be  cooled 
1°  its  volume  will  be  diminished  4  j,T  part,  2°,  4£  1 ,  and 
so  on  down.  Another  way  of  stating  this  is  to  say  that 
4'Jl  cubic  inches  of  a  gas  at  32°  become  492  when 
raised  1°,  493  when  raised  2°,  and  in  every  case  the 
volume  is  491  -4-  ^  t  being  the  number  of  degrees  above 
32°.  In  cooling,  also,  491  cubic  inches  become  490 
at  31°,  489  at  30°,  and  so  on.  These  are  results 
obtained  by  experiment,  and  this  number  491  indi- 
cates that  at  491°  below  the  freezing  point  the  gas 
would  cease  to  exist,  —  not  that  the  matter  would  be 
annihilated,  but  that  it  would  be  no  longer  in  the 
gaseous  state.  This  point  of  temperature,  491°  below 
the  freezing  point  of  water,  or  459°  below  the  zero  of 
the  Fahrenheit  scale,  is  called  Absolute  Zero,  a  term 
which  means  the  total  absence  of  any  degree  of  heat. 
One  may  reckon  the  temperature  of  bodies  in  general 
on  this  basis,  and  then  the  temperature  is  called  the 
absolute  temperature.  For  instance,  the  absolute  tem- 
perature of  freezing  water  is  491°,  of  boiling  water 
459  -f  212  =  671°,  of  the  human  body  459  +  98.6 
=  5o7.6°. 

The  behavior  of  gases  in  thus  expanding  and  con- 
tracting with  reference  to  such  an  absolute  zero  has 
been  formulated  into  a  statement  which  may  be 
remembered  easily.  The  volume  of  a  yas  is  proportional 
to  its  absolute  temperature.  This  is  called  the  Law  of 
Charles.  Its  utility  may  be  seen  by  an  example.  A 
cubic  foot  of  air  at  32°  is  heated  to  100°,  what  volume 
will  it  now  occupy? 

The  absolute  temperatures  of  the  two  volumes  are 


88  NATURAL   PHILOSOPHY. 

as  follows:  that  for  32°F.  =  491°,  that  for  100° F. 
=  491  +  68  =  558°. 

As  the  volumes  will  be  proportional  to  these  numbers 
we  have  491  :  558  ::  1  :  ^  =  1.14  cubic  feet,  nearly. 

What  will  be  the  volume  of  air  to  which  a  cubic  foot 
will  be  reduced  when  its  temperature  is  lowered  from 
75°  to  0°  ?  The  corresponding  absolute  temperatures 
will  be  491  -f  43  =  534  and  491  —  32  =  459.  Then 
534  :  459  ::  1  :  x=  -859  of  a  cubic  foot. 

How  much  air  will  escape  from  a  room  20  feet 
square  and  10  feet  high  when  its  temperature  is  raised 
from  40°  to  70°?  Volume  of  the  room  is  20  X  20  X  10 
=  4000  cubic  feet.  Absolute  temperatures  of  the  two 
extremes  are 

491  +  8  =  499,  and  491  -f  38  =  529. 

499  :  529  ::  4000  :  %  =  4240  =  expanded  air. 

4240  —  4000  =  240  =  cubic  feet  escaped. 

II.  Conduction.  —  If  the  end  of  a  rod  of  iron  be 
thrust  into  the  fire,  the  end  held  in  the  hand  will 
presently  become  too  hot  to  be  held,  unless  the  rod  be 
a  long  one  ;  the  heat  slowly  creeps  along  the  rod, 
molecule  by  molecule.  The  process  is  called  Conduc- 
tion, for  the  molecules  must  be  in  cohesive  contact  in 
order  that  heat  may  travel  from  one  to  the  other.  But 
different  substances  have  very  different  rates  of  conduc- 
tion, silver  and  copper  being  very  good,  while  German 
silver,  wood,  and  paper  are  relatively  poor.  All  the 
objects  upon  the  table  may  be  at  the  same  temperature, 
but  to  the  touch  they  may  seem  to  be  different ;  the 
better  the  conducting  power,  the  colder  the  object  will 


ON   HEAT.  89 

appear  to  be,  as  it  robs  the  hand  of  its  heat,  conducting 
it  away  at  a  swifter  rate  than  poorer  conductors  can. 
Furs  and  feathers,  being  poor  heat  conductors,  serve  to 
prevent  the  loss  of  bodily  heat  of  animals  and  birds, 
while  our  clothing,  varying  with  the  season,  serves  the 
same  purpose  for  us. 

III.  Specific  Heat. —  The  specific  heat  of  a  substance 
is  the  amount  of  heat  it  takes  to  raise  the  temperature 
of  a  pound  of  it  one  degree,  compared  with  the  amount 
required  for  the  same  weight  of  water  taken  as  unity. 
Thus  a  body  requiring  but  half  as 
much  would  have  its  specific  heat  =  .5. 
The  heat  required  for  heating  a  pound 
of  water  one  degree  is  called  a  heat 
unit,  which  has  a  mechanical  equiva- 
lent of  778  foot-pounds.  The  specific 
heat  of  a  substance  is  then  the  ratio 
of  its  heat  unit  per  pound  to  that  of 
water  per  pound. 

1.  Of  Gases.  When  a  gas  is  heated, 
and  thus  its  molecules  have  swifter  free-path  motion 
Imported  to  them,  they  strike  upon  the  walls  of  the 
containing  vessel  with  greater  velocity  and  produce  a 
correspondingly  greater  pressure  ;  they  have  more 
energy.  Suppose  ecdf  (Fig.  27)  be  a  vessel  in  which 
the  partition  ab  fits  air-tight,  but  is  capable  of  moving 
up  and  down  freely.  Let  acdb  represent  a  cube  one 
foot  on  a  side  so  as  to  contain  a  cubic  foot  of  air  at  32°, 
which  is  the  temperature  outside.  The  pressure  will  be 
the  same  on  both  sides  of  ab.  If  heat  be  applied  to  the 


90  NATURAL   PHILOSOPHY. 

enclosed  air  while  the  partition  ab  is  held  firmly  in  place 
so  that  the  air  cannot  expand,  it  will  require  a  certain 
definite  amount  of  heat  to  raise  the  temperature  of  the 
contained  air  one  degree.  But  if  the  partition  be  per- 
mitted to  move,  the  increased  pressure  due  to  heat  will 
raise  it  somewhat,  but  in  raising  the  partition  it  will  be 
doing  work  against  the  pressure  of  the  air ;  pressure 
upon  the  square  inch  being  14.7  pounds,  upon  the  square 
foot  surface  it  is  144  X  14.7  =  2116  pounds,  and  the 
amount  of  work  pd  will  equal  the  product  of  2116 
into  the  distance  the  partition  will  be  raised.  It  is 
found,  however,  that  when  by  expanding  the  air  does 
work,  it  requires  more  heat  to  raise  its  temperature 
one  degree  than  when  it  does  not  expand,  in  the  ratio 
of  1.41  :  1. 

The  ratio  of  the  number  of  foot-pounds  of  energy 
required  to  raise  a  pound  of  the  gas  one  degree  in 
temperature,  to  778  : 

(1)  In  an  open  vessel,  doing  work  against  air-pres- 
sure, is  called  specific  heat  under  constant  pressure. 

(2)  In  a  tight  vessel,  doing  no  work,  is  called  specific 
heat  under  constant  volume. 

For  specific  heat  under  constant  pressure  it  is  .2375. 
For  specific  heat  under  constant  volume  it  is  .1674,  and 
1111  =  1.41.  For  example:  To  raise  the  temperature 
of  a  pound  of  air  one  degree,  when  the  air  could  not 
expand,  would  require  .1674  as  much  as  a  pound  of 
water  would  require  in  being  heated  one  degree,  or 
778  X  .1674  =  130.2  foot-pounds;  when  it  could  ex- 
pand it  would  require  1.41  times  as  much:  .1674  X  1.41 
=  .2360,  and  778  X  .2360  =  183.6  foot-pounds. 


ON   HEAT.  91 

This  means  that  when  a  gas  is  heated  in  a  tight 
enclosure  where  it  cannot  expand,  all  the  energy  is 
employed  in  heating  the  molecules  ;  where  expansion 
can  take  place,  a  part  of  the  energy  of  the  heated 
molecules  is  expended  at  once  in  doing  work,  and  it 
therefore  requires  more  heat  to  bring  the  temperature 
to  the  same  point,  and  in  the  above  ratio. 

Whenever  a  gas  does  work  it  always  loses  temperature, 
as  the  energy  for  doing  the  work  comes  from  the  heat 
in  the  gas.  The  translatory  motion  represented  in  the 
work  is  the  transformed  vibratory  motion  of  the  mole- 
cules. It  is  this  that  makes  possible  steam-,  gas-,  and 
air-engines. 

2.  Of  Solids.  How  much  work  in  foot-pounds  is 
needful  to  raise  the  temperature  of  a  pound  of  water 
one  degree  has  been  shown  to  be  778,  but  no  other 
substance  requires  so  much.  How  much  any  given 
substance  requires  can  be  found  by  taking  a  pound  of 
it,  raising  its  temperature  one  hundred  degrees,  and 
then  plunging  it  into  a  pound  of  water  and  observing 
to  what  temperature  the  water  rises.  Suppose  a  pound 
of  mercury  at  212°  be  cooled  in  water  at  32°;  the 
mixture  is  found  to  have  the  temperature  of  37.9°. 
The  water  has,  then,  been  warmed  5.9°,  while  the 
mercury  has  lost  174.1,  and  the  ratio  of  174.1  to  5.9 
is  as  1  :  .033  ;  that  is,  the  amount  of  heat  needed  to 
raise  the  temperature  of  a  pound  of  mercury  one  degree 
is  only  one-thirtieth  that  required  for  the  same  weight 
of  water. 

The  specific  heat  of  water  is  taken  as  the  standard 
and  is  called  unity,  or  1.  As  it  is  higher  than  that  of 


92  NATURAL   PHILOSOPHY. 

any  other  liquid  or  solid  substance  the  others  will  be 
fractional. 

The  specific  heat  of  a  number  of  substances  is  given : 

^yate^ 1.0000 

Ice 4900 

Iron 1138 

Copper .0939 

Silver 0570 

Lead 0314 

Specific  Energy  of  Gaseous  Molecules.  —  The  heat 
energy  of  a  molecule  of  hydrogen  is  the  same  as  that 
of  a  molecule  of  oxygen  when  they  have  the  same 
temperature,  but  hydrogen  being  only  one-sixteenth  as 
heavy  must  have  sixteen  times  as  many  molecules  to 
the  pound.  Hence  a  given  weight  of  hydrogen  will 
have  sixteen  times  as  much  energy  as  the  same  weight 
of  oxygen.  In  order,  then,  to  produce  a  rise  of  temper- 
ature of  one  degree  in  a  pound  of  hydrogen,  sixteen 
times  as  much  heat  is  needed  as  for  the  same  weight  of 
oxygen.  The  specific  heat  of  hydrogen,  then,  is  sixteen 
times  that  of  oxygen.  In  general,  the  lighter  the  mole- 
cules of  a  gas  the  more  numerous  must  they  be  in  a 
pound  of  the  substance,  and  the  higher  must  be  its 
specific  heat. 

Specific  Heat  of  Solid  Elements.  —  The  specific 
heat  of  an  element  varies  inversely  as  its  atomic 
weight,  or  the  product  of  the  specific  heat  into  the 
atomic  weight  equals  a  constant  quantity  which  is 
about  6.4  ;  thus  the  atomic  weight  of  lead  is  207,  its 
specific  heat  is  .0314  and  207  X  -0314  =  6.43.  If  this 


ON    HEAT.  93 

numb'er  6.4  be  divided  by  the  specific  heat  of  an 
element  it  will  give  the  atomic  weight,  and  that  is  one 
way  chemists  employ  to  determine  atomic  weights. 

The  specific  heat  of  a  substance  determines  how 
high  its  temperature  will  rise  when  a  definite  amount 
of  heat  or  of  work  is  spent  upon  it.  For  instance,  it 
requires  778  foot-pounds  of  work  to  be  done  upon  a 
pound  of  water  to  raise  its  temperature  one  degree. 
If  778  foot-pounds  of  work  were  done  upon  a  pound  of 
iron,  its  temperature  would  be  raised  above  that  of 
water  in  proportion  as  its  specific  heat  is  lower  ;  that  is, 
.^  =  9.02°. 

A  lead  bullet  weighing    an   ounce   strikes  a  target 
with  a  velocity  of  a  1000  feet  a  second.     How  high  is 
it  heated  by  the  impact,    if  one-half  of    the  energy  is 
spent  on  it,  the  other  half  on  the  target? 
wv*      TV  X  10002 


T 
= 


=9i6  foot-pounds. 


976  foot-pounds  spent  upon  a  pound  of  water  would 
raise  its  temperature  £||  =  1.25°;  if  spent  on  an  ounce 
it  would  raise  it  1.25  X  16  =  20°.  If  spent  on  lead 
having  specific  heat  of  .0314,  its  temperature  would  be 
raised  .r,|£4  =636°;  but  if  one-half  be  spent  on  the 
target  it  will  be  6|^-  =  318°  =  the  rise  in  temperature 
of  the  bullet. 

One  may  now  by  careful  thinking  understand  how 
molecules  of  different  kinds  may  have  the  same  amount 
of  energy  in  the  form  of  heat  when  their  temperatures 
are  the  same,  for  if  their  atomic  weights  are  different 
they  must  have  different  degrees  of  amplitude  of  vibra- 
tion, —  that  is,  their  velocities  must  be  different;  yet 


94  NATURAL   PHILOSOPHY. 

when  equal  weights  of  different  elements  are  taken, 
they  differ  very  much  in  their  capacity  for  heat. 

IV.  Changes  of  State.  —  Solid  to  Liquid.  The  states 
of  matter  have  been  described  as  solid,  liquid,  and 
gaseous,  and  it  is  one  of  the  properties  of  heat  to 
change  solids  to  liquids  or  gases. 

That  ice  is  frozen  water  and  that  it  may  be  again 
changed  into  water  is  familiar  enough  to  every  one. 
Now  that  more  definite  knowledge  is  possessed  of  heat 
and  its  mode  of  action  it  becomes  possible  to  explain 
how  the  changes  are  effected. 

The  distinction  between  a  solid  and  a  liquid  is,  that 
the  molecules  in  the  solid  cohere  so  strongly  together 
that  they  are  not  easily  pulled  apart,  so  that  if  one  part 
of  a  solid  body  is  pushed  or  pulled  the  pressure  is  felt  by 
the  whole  body  which  will  move  as  a  whole  if  part  of  it 
is  ;  this  is  not  the  case  with  a  fluid. 

Let  one  now  consider  the  molecules  of  any  solid,  as, 
for  instance,  ice  at  the  temperature  of  31°.  In  a  cubic 
inch  of  it  there  are  a  certain  number  of  molecules,  and 
eacli  one  has  a  definite  position,  rate,  and  amplitude  of 
motion.  If  that  amplitude  be  increased  they  will  bum]) 
upon  each  other  harder  and  will  bound  away  from  each 
other  with  greater  velocity,  and  when  they  bound  away 
so  far  on  the  average  that  they  get  out  of  each  others 
range  of  cohesion,  the  molecules  can  be  individually 
moved  without  pushing  or  pulling  their  neighbors  —  the 
body  is  no  longer  a  solid.  The  heat  which  is  applied 
to  melt  ice  does  this.  Indeed,  the  increase  of  ampli- 
tude of  vibration  destroys  the  cohesion,  so  that  when 


ON    HEAT.  95 

this  reaches  a  certain  degree  any  further  increase  of 
the  energy  results  in  changing  the  ice  to  water  instead 
of  raising  the  temperature.  In  'Similar  manner,  when 
water  is  reduced  to  32°  its  molecules  are  on  the  bound- 
ary such  that  any  further  decrease  of  individual  motion 
1  nin^s  them  within  cohesion  distance,  and  then  the 
water  becomes  solid.  What  is  true  for  water  and  ice 
is  true  for  iron,  lead,  gold,  rocks,  indeed  most  bodies, 
the  difference  between  them  being  chiefly  in  the  tem- 
perature at  which  such  change  of  condition  takes  place. 
When  a  solid  becomes  liquid  the  process  is  called 
fusion,  melting,  or  liquefaction.  When  a  liquid  be- 
comes a  solid  the  process  is  called  freezing,  or  congeala- 
tion.  For  a  given  substance  fusion  and  solidification 
take  place  at  the  same  temperature ;  thus,  ice  fuses  and 
water  solidifies  at  32°. 

The  melting  point  of  some  of  the  elements  is  given 
on  page  5.  If  iron  melts  at  3000°,  then  iron  cannot 
remain  solid  when  the  temperature*  is  higher  than  that, 
and  in  like  manner  when  the  temperature  is  below  32° 
water  becomes  ice.  If,  as  is  probable,  the  earth  was 
once  hotter  than  3000°,  there  could  not  have  been  any- 
thing solid  upon  it.  The  waters  of  the  oceans  would 
have  existed  as  steam.  The  lava  that  flows  from  vol- 
canoes is  melted  rock  and  implies  a  temperature  of  two 
or  three  thousand  degrees.  On  the  other  hand,  in  the 
polar  regions  the  ice  never  melts ;  and  on  the  dark  side 
of  the  moon,  where  the  sun  never  shines,  the  tempera- 
ture is  probably  a  hundred  degrees  below  zero,  or  more. 

As  a  general  thing  the  colder  a  body  is  the  stronger 
is  its  cohesion  ;  it  takes  a  greater  pull  to  break  a  wire 


96  NATURAL   PHILOSOPHY. 

at  32°  than  at  50°,  and  still  greater  to  break  it  at  0°. 
This  increase  in  cohesion  is  found  experimentally  to 
hold  good  down  to  —300°. 

Influence  of  Pressure  on  Fusion.  —  It  has  been 
found  that  pressure  upon  a  body  changes  its  fusing 
temperature,  usually  raising  it.  If  the  heat  applied 
to  melt  a  body  has  to  do  work  against  pressure,  one 
would  expect  that  more  heat  would  be  required  ;  in  the 
same  way  and  for  the  same  reason,  more  is  required  to 
raise  the  temperature  of  air  when  it  can  expand  and  do 
work  than  when  it  does  not  have  to  do  so.  Thus,  if 
it  requires  a  temperature  of  2000°  to  fuse  common 
rock  material  in  the  air,  to  melt  it  when  subjected  to 
a  pressure  of  some  tons  per  square  inch  may  require 
2500°. 

The  deeper  one  goes  into  the  earth  the  warmer  it 
becomes,  increasing  at  the  rate  of  about  one  degree  in 
each  60  feet.  At  that  rate  the  temperature  at  the  depth 
of  25  miles  would  be  above  2000°,  quite  sufficient  to  melt 
rock  if  it  were  on  the  surface  where  the  pressure  is  at 
most  but  about  15  pounds  per  square  inch.  But  as  one 
goes  down  into  the  earth  the  rock-pressure  increases 
also,  and  much  more  rapidly  than  the  temperature,  the 
result  being  that  the  rocks  cannot  be  melted,  no  matter 
what  the  temperature.  This  means  that  the  earth  is 
solid  to  the  center,  and  not,  as  has  sometimes  been 
thought,  liquid  in  the  interior,  with  a  relatively  thin 
crust  on  which  we  live. 

Liquid  to  Gaseous.  The  difference  between  the  liquid 
and  the  gaseous  state  is  the  difference  between  very 


ON    HEAT.  97 

slight  cohesion  and  none  at  all.  If,  therefore,  the  tem- 
perature of  a  liquid  be  raised  so  as  to  increase  the 
average  distance  apart  of  all  the  molecules  —  altogether 
beyond  the  range  of  cohesion  —  they  will  fly  off  and 
become  free  roving  gaseous  molecules,  and  will  main- 
tain this  condition  so  long  as  such  temperature  be  kept 
up.  The  vibratory  heat  energy  imparts  translatory 
mechanical  energy  to  the  molecules  and  they  bound 
a  way.  This  makes  the  difference  between  the  liquid 
and  the  gaseous  state  —  simply  the  amount  of  energy 
present  among  the  molecules.  After  ice  has  become 
water,  the  molecular  cohesion  is  very  small,  yet  it  has 
some  value ;  but  as  the  temperature  is  raised  the  cohe- 
sion becomes  less  and  less,  until  at  212°  it  reaches  the 
limit,  where  the  molecules  no  longer  cohere,  but  become 
free  and  gaseous.  In  doing  this  they  necessarily  occupy 
much  greater  space,  so  that  a  cubic  inch  of  water 
becomes  nearly  a  cubic  foot  of  gaseous  steam.  Some- 
times it  is  called  a  vapor,  but  there  is  no  distinction 
between  a  gas  and  a  vapor.  The  free  paths  of  such 
molecules  are  now  something  like  250  times  their  own 
diameters.  Such  rapid  increase  in  volume  implies  vibra- 
tory amplitude  of  molecular  motion  so  great  as  to  quite 
destroy  cohesion  among  the  colliding  molecules. 

Dissociation.  This  process  can  be  carried  on  another 
step  by  increase  of  temperature.  Water  molecules  are 
made  up  of  two  atoms  of  hydrogen  combined  with  one 
atom  of  oxygen  cohering  together.  If  the  amplitude 
of  vibration  of  the  individual  atoms  in  the  molecule  be 
increased  by  increasing  their  temperature,  it  will  pres- 
ently reach  a  limit  at  which  the  atoms  are  no  longer 


98  NATURAL   PHILOSOPHY. 

able  to  remain  together,  —  they  separate  ;  that  is,  the 
water  molecule  is  broken  up,  and  the  atoms  become 
individual  gaseous  particles.  This  happens  at  about 
4500°.  This  process  is  called  dissociation. 

Evaporation.  Consider  the  surface  of  water  in  a 
saucer.  It  is  in  contact  with  the  air  above  it.  The  air 
particles  are  bumping  upon  the  surface  molecules,  but 
no  water  molecule  is  thus  struck  downward  contin- 
uously with  the  same  degree  of  impact.  The  surface 
molecules  of  the  water  are  continuously  being  bumped 
from  below  upwards,  for  they  are  in  practical  contact 
with  other  molecules  except  above,  and  any  such  bump 
from  below  upon  a  surface  molecule,  occurring  at  an 
instant  when  there  is  no  corresponding  downward  bump 
of  an  air  particle,  may  cause  that  water  molecule  to  be 
quite  knocked  away  from  the  surface,  and  so  become  a 
free  gaseous  molecule.  The  less  frequent  the  number 
of  bumps  from  the  air  downward,  that  is,  the  rarer  the 
air,  the  greater  the  number  of  water  molecules  which 
will  be  driven  from  the  surface.  This  process  of 
changing  a  liquid  to  the  gaseous  form  is  called  evapo- 
ration. It  is  going  on  all  the  time  from  the  surfaces  of 
liquids  and  many  solids,  and  at  all  temperatures,  for 
even  ice  will  evaporate.  The  wet  clothes  upon  the 
line  may  freeze  at  first,  but  will  presently  dry,  if  left 
alone.  A  lump  of  camphor,  if  left  in  free  air,  will 
slowly  be  evaporated,  and  the  metal  mercury  likewise, 
though  at  a  very  low  rate ;  in  any  case,  evaporation 
depends  upon  the  temperature. 

Solidification.  At  very  high  temperatures,  such  as 
that  of  the  sun  and  of  an  electric  arc,  every  kind  of 


ON    HEAT.  99 

substance  we  are  acquainted  with  is  reduced  to  its 
gaseous  form  ;  so,  on  abstracting  the  heat  from  such 
bodies,  they  assume  the  solid  form  again,  for  the  free 
path  <>f  their  molecules  is  shortened  until  the  molecules 
are  within  cohesion  distance.  Most  of  the  chemical 
elements  are  to  be  found  in  the  solid  state;  but  hydro- 
gen, oxygen,  and  nitrogen,  as  well  as  common  air, 
require  that  the  temperature  be  very  low,  and  that 
pressure  be  applied  in  order  to  reduce  then;  to  the 
Ijquid  or  solid  form.  In  this  particular  they  do  not 
differ  in  quality  from  other  substances  except  in  degree, 
—  they  assume  the  gaseous  condition  at  a  lower  tem- 
perature. At  the  temperature  of  — 300°  both  oxygen 
and  common  air  have  been  solidified,  and  as  they  are 
magnetic,  they  will  stick  in  masses  to  the  poles  of  a 
magnet,  as  iron  will  do,  and  slowly  evaporate  as  they 
become  warmer. 

It  was  stated  on  page  79  that  when  hydrogen  and 
oxygen  unite  to  form  water  they  give  up  an  immense 
amount  of  energy  in  the  form  of  heat.  Obviously,  they 
cannot  give  up  energy  which  they  do  not  possess ;  hence 
one  must  think  of  these  gases  as  possessing  a  great,  but 
definite,  amount  of  energy  at  ordinary  temperatures,  en- 
ergy which  is  not  heat,  but  may  be  transformed  into  heat. 

It  is  thought  by  some  to  be  probable  that,  if  these 
and  all  other  gases  could  have  their  temperatures 
reduced  to  absolute  zero,  they  would  cease  to  be 
gaseous  in  form,  and  their  molecules  would  sink  to 
the  ground  like  so  much  dust.  This  conclusion  follows 
from  the  consideration  that  it  is  heat  alone  that  keeps 
any  molecules  in  the  gaseous  state. 


100 


NATURAL    PHILOSOPHY. 


Crystallization,  A  large  number  of  substances  assume 
some  regular  form  on  becoming  solid  from  either  the 
liquid  or  gaseous  state.  Such  symmetrical  forms  are 
called  crystals.  Ice  is  such  a  crystalline  form,  us  may 
be  seen  in  the  fern-like  shapes  upon  the  window  panes 
on  a  cold  day,  and  snowflakes  have  a  hexagonal  form 
with  six  points  or  six  sides  in  many  varieties  (Fig.  28). 


More  than  a  hundred  have  been  pictured.  Sulphur, 
alum,  and  sugar  are  substances  that  easily  crystallize. 
Quartz,  diamonds,  and  most  minerals  are  frequently 
found  crystallized. 

A  strip  of  zinc  thrust  into  a  beaker  or  bottle  contain- 
ing dilute  lead  acetate  will  be  covered  in  a  few  minutes 
with  a  dense  growth  of  lead  leaves  looking  like  vege- 
table forms.  A  drop  of  a  solution  of  ammonium 


ON    HEAT.  101 

chloride  spread  upon  a  strip  of  glass  and  looked  at 
through  a  magnifying  glass  will  be  seen  to  assume  an 
arrangement  like  the  streets  of  a  city,  and  a  solution  of 
Uiriuni  chloride  will  have  the  appearance  of  a  lot  of 
small  hushes.  If  projected  upon  a  screen  by  means 
of  the  porte-lumiere  and  a  beam  of  sunlight  (p.  230), 
they  may  be  seen  to  great  advantage  by  a  room  full 
of  people. 

The  ability  to  assume  such  regular  shapes  is  inherent 
in  the  molecules,  and  depends  largely  upon  the  tem- 
perature, for  at  a  definite  temperature  liquids  will  dis- 
solve only  a  certain  quantity  of  a  substance,  and  if  the 
temperature  be  made  lower  some  of  the  substance  will 
become  solid  in  the  crystallized  form.  Solid  iron  will 
crystallize  if  it  be  jarred  often,  which  shows  that  the 
molecules  are  all  the  time  under  some  sort  of  con- 
straint, which  tends  to  set  them  in  symmetrical  order, 
and  jarring  helps  them  to  assume  their  more  stable 
positions. 

Cooling.  There  are  two  methods  by  which  a  body 
may  lose  its  heat,  —  by  conduction  and  by  radiation. 
The  first  implies  contact  with  a  cooler  mass  of  matter, 
arid  the  second  a  transformation  of  the  heat  energy  into 
ether  wave  energy,  sometimes  called  radiant  energy. 
In  this  place  we  are  concerned  only  with  the  former. 
A  heated  body,  if  left  to  itself,  will  cool  to  the  tempera- 
ture of  surrounding  bodies ;  it  will  not  get  any  colder. 
Out  of  doors  the  temperature  in  summer  may  be  70° 
or  80°.  In  winter  it  may  fall  to  zero  or  lower. 

The  conditions  equalize  the  temperatures  of  all 
bodies  exposed  to  them,  except  such  as  are  provided 


102  NATURAL   PHILOSOPHY. 

with  some  other  means  for  changing  them.  If  one 
blows  his  breath  upon  the  back  of  the  hand  it  will  feel 
cool,  although  the  breath  is  several  degrees  warmer 
than  the  hand.  If  a  drop  of  water  be  spread  over  the 
hand  it  will  feel  cool,  and  if  this  be  blown  upon,  it  will 
be  still  cooler.  All  this  happens  because  evaporation 
is  going  on.  In  order  that  the  moisture  upon  the  hand 
shall  become  gaseous,  it  must  have  heat  from  some 
source  ;  the  hand  supplies  it,  and  the  feeling  of  cool- 
ness results.  Blowing  upon  it  increases  the  rate  of 
evaporation.  A  drop  of  alcohol  or  of  ether  placed  upon 
the  bulb  of  a  thermometer  will  lower  the  temperature 
of  the  bulb  several  degrees. 

In  like  manner,  when  solids  become  liquids  heat  is 
abstracted  from  the  surrounding  body.  Ice  and  salt, 
both  solids,  will  melt  if  mixed  together,  and  in  becom- 
ing liquid  will  abstract  heat  from  any  available  source. 
Water  may  be  frozen  by  enclosing  it  in  such  a  mixture. 
This  is  the  common  arrangement  for  making  ice  cream. 
Salt  water  does  not  freeze  at  32°;  at  how  much  lower 
temperature  it  may  remain  liquid  depends  upon  the 
amount  of  salt  dissolved.  With  such  a  mixture  the 
temperature  may  fall  to  0°  F. 

Many  substances  will  dissolve  in  water  more  rapidly 
if  the  water  be  heated.  If  the  water  be  not  heated  the 
solution  will  go  on  at  a  slower  rate,  and  the  temperature 
of  the  mixture  will  fall.  Thus,  add  some  ammonium 
chloride  to  an  equal  volume  of  water  at  ordinary  tem- 
perature, and  stir  it  with  the  bulb  of  a  thermometer. 
The  temperature  will  fall  15  or  20  degrees.  The  heat 
needed  for  dissolving  it  comes  from  outside,  from  the 


ON    HEAT.  103 

hand  or  air  or  both,  so  the  reduction  of  the  solid  to 
the  liquid  form  is  a  cooling  process  for  neighboring 
bodies. 

\Vlirn  air  is  condensed  it  is  heated,  as  shown  by  the 
experiment  on  page  71.  If  it  be  allowed  to  expand 
again  at  once,  it  regains  its  original  temperature  ;  but 
if  it  be  allowed  to  stand  after  condensation  until  it  has 
cooled  to  the  temperature  of  surrounding  things,  and 
then  permitted  to  expand,  its  temperature  falls,  and 
water  in  contact  may  be  thus  frozen.  More  heat  is 
needed  to  maintain  air  as  a  rare  gas  than  as  a  denser 
one. 

Surface  Tension.  The  fact  that  the  surface  mole- 
cules of  liquids  are  subject  to  cohesive  attraction  only 
at  their  sides  and  underneath  enables  them  to  cohere 
together  stronger  than  those  beneath  the  surface  do  ; 
the  energy  which  is  divided  in  every  direction  by  one 
beneath  the  surface  is  divided  among  a  smaller  number 
on  the  surface,  and  is  therefore  stronger.  This  gives 
to  the  liquid  surface  a  tension,  acting  much  like  a  thin 
skin,  always  tending  to  contract  the  surface  to  the 
smallest  dimensions.  A  soap-bubble  shows  this,  for  if 
blown  and  left  on  the  bowl  of  the  pipe  it  will  contract 
so  much  as  to  enter  the  bowl.  The  globular  form  of  a 
drop  of  water  is  due  to  the  same  condition.  The  sur- 
face tension  of  a  liquid  serves  to  restrain  evaporation, 
so  that  it  cannot  go  on  at  as  swift  a  rate  as  it  would  if 
the  temperature  alone  controlled  it.  Pure  water  has 
so  high  a  surface  tension  that  bubbles  cannot  be  blown 
with  it;  but  a  little  soap  in  it  reduces  the  tension  very 
much,  and  increases  the  rate  of  evaporation  as  higher 


104  NATURAL    PHILOSOPHY. 

temperature  would  do.  Almost  anything  water  will 
dissolve  acts  to  thus  reduce  its  surface  tension. 

Fill  a  saucer  with  pure  water  and  scatter  some  lyco- 
podium  powder  or  dust  on  its  surface.  A  drop  of  ether 
on  a  glass  rod  held  an  inch  or  two  above  will  cause  a 
lively  scattering  of  the  particles,  as  if  repelled  by  the 
rod.  The  ether  vapor  is  denser  than  the  air,  and  falls 
to  the  surface  of  the  water ;  it  is  at  once  absorbed  by 
the  water  lessening  its  surface  tension,  and  the  part  of 
the  surface  not  thus  affected  pulls  the  particles  away. 

A  few  small  crumbs  of  camphor  dropped  upon  the 
surface  of  pure  water  will  move  about  in  a  surprising 
way  as  if  alive.  The  camphor  is  dissolved  by  the  water 
at  the  points  of  contact,  and  this  reduces  the  tension  at 
those  points,  and  the  changes  in  tension  result  in  pull- 
ing the  bite  about  at  a  lively  rate. 

A  drop  of  any  of  the  essential  oils,  such  as  those  of 
cinnamon,  clove,  or  creosote,  when  dropped  on  a  water 
surface,  spreads  about  and  assumes  characteristic  forms 
\vhieh  enable  one  to  identify  these  oils,  as  each  has  its 
own  characteristic  tension  and  cohesion. 

The  Boiling  Point.  —  Whenever  heat  energy  is 
applied  to  a  liquid  in  any  way  in  sufficient  quantity 
so  that  beneath  its  surface  the  molecular  cohesion  is 
rapidly  destroyed,  bubbles  are  formed  by  the  gaseous 
molecules  which  rise  to  the  surface  and,  if  free,  escape 
into  the  air.  If  the  liquid  be  water,  and  it  lie  in  an 
enclosed  vessel  like  a  boiler  from  which  the  gaseous 
molecules,  called  steam,  cannot  escape,  the  pressure 
will  rise,  and  the  steam  with  its  temperature  and 


ON    HEAT.  .  105 

pressure  may  be  conveyed  by  pipes,  and  used  to  warm 
houses  or  drive  engines. 

The  boiling  point  of  water  is  212*  the  same  tem- 
.perature  at  which  steam  will  again  condense  to  water 
on  removing  some  of  its  energy.  Other  liquids  have 
other  boiling  points;  thus,  alcohol  boils  at  140°,  ether 
at  63°,  mercury  at  630°,  lead  at  2700°. 

Pressure  affects  the  boiling  point  of  liquids  very 
much  as  it  affects  the  fusing  point  of  solids,  —  it  raises 
it.  If  a  flask  of  water  at  200°  be  placed  under  the 
receiver  of  an  air-pump,  and  the  air-pressure  be  removed, 
the  water  will  boil  at  as  lively  a  rate  as  if  still  over  a 
fire.  At  high  elevations,  where  the  air-pressure  is  less, 
water  boils  at  a  lower  temperature  than  212°.  In  the 
city  of  Mexico,  7470  feet  above  the  sea-level,  water 
boils  at  199°.  In  Quito,  South  America,  9340  feet 
high,  it  boils  at  195°,  and  on  the  top  of  Mt.  Blanc, 
15,630  feet,  at  182°. 

If  we  have  steam  and  water  at  212°,  it  is  evident 
that  there  is  much  more  energy  in  the  steam  molecules 
than  there  is  in  the  water  molecules,  for  the  steam  has 
energy  of  free-path  motion  in  addition  to  its  internal 
vibratory  rate  that  constitutes  its  temperature  ;  this 
extra  energy  that  the  molecules  of  steam  have,  when 
their  temperature  is  the  same  as  that  of  the  water  from 
which  the  steam  was  formed,  is  called  its  latent  heat. 
It  means  only  that,  in  becoming  water  again,  it  will 
give  out  the  same  amount  of  energy  in  the  form  of  heat, 
or  that  the  mechanical  energy  of  the  steam  molecule, 
represented  by  its  free-path  motion,  will  be  changed 
into  heat  energy  when  it  is  again  allowed  to  assume 


106  NATURAL    PHILOSOPHY. 

the  liquid  form..  In  like  manner,  when  water  at  32° 
becomes  ice  at  32°,  it  gives  up  a  relatively  large 
amount  of  energy,  the  same  in  amount  that  was  needed 
to  change  it  from  ice  to  water.  This,  too,  has  been 
called  latent  heat,  but  it  signifies  only  a  change  in  the 
form  of  the  energy,  and  not  that  there  is  heat  in  the 
molecule  which  is  latent.  If  a  pound  of  ice  and  a 
pound  of  water,  each  at  32°,  be  exposed,  in  two  similar 
vessels,  to  the  same  source  of  heat,  at  the  moment  the 
ice  is  melted  in  the  one  the  temperature  of  the  other 
will  be  174°;  showing  that  it  takes  as  much  heat  to 
melt  a  pound  of  ice  as  it  does  to  raise  a  pound  of  water 
from  32°  to  174°,  that  is,  142  heat  units.  In  like 
manner,  if  a  pound  of  water  at  212°  be  mixed  with  a 
pound  of  pulverized  ice  or  snow  at  32°,  when  the  latter 
is  melted  the  mixture  will  have  the  temperature  of 
only  50°.  The  ice  will  have  gained  18°,  while  the 
water  will  have  lost  162°.  Here  again  142  heat  units 
have  been  consumed  in  changing  the  ice  to  water. 

When  steam  at  212°  is  converted  to  water  at  212°  it 
yields  up  energy  which  takes  the  form  of  heat. 

A  pound  of  steam  at  that  temperature  becomes  water 
at  the  same  temperature  on  giving  up  966  heat  units. 

See,  then,  the  energy  measured  in  heat  units  which  is 
imparted  to  a  pound  of  ice  in  raising  it  to  steam. 

From  ice  at  32°  to  water  at    32°=  142  heat  units. 
From  water  at    32°  to  water  at  21 2°  =  1 80          " 
From  water  at  21 2°  to  steam  at  21 2°  =966          " 
Total,    1288 

The  number  1288  X  778  =  1,002,064  foot-pounds  of 


ON    HEAT.  107 

energy  spent  on  one  pound  of  ice,  and  this  quantity  it 
will  give  out  as  heat  on  cooling  down  to  ice  again. 

VII.  The  Working  Power  of  Steam. —  On  page  106 
it  is  pointed  out  how  much  energy  in  footpounds  is 
spent  in  raising  a  pound  of  ice  to  steam  at  212°.  At 
this  temperature  the  pressure  of  the  steam  is  the  same 
as  that  of  the  air,  namely,  about  15  pounds  per  square 
inch.  If  water  is  boiled  while  exposed  to  the  air  the 
pressure  never  rises  higher  than  this,  but  if  the  water 
is  enclosed  in  an  air-tight  vessel  or  boiler,  and  heat  still 
be  applied,  the  pressure  rises,  and  reacting  upon  the 
water  stops  the  boiling  until  more  heat  be  supplied ; 
so  when  heat  is  abundant  the  temperature  of  the  boiling 
water  rises  so  that  at  260°  the  pressure  is  20  pounds 
alx)ve  atmospheric  pressure,  at  308°  it  is  60,  and  at 
365°  it  is  150  pounds  per  square  inch  above  the  15 
pounds  pressure  of  the  atmosphere. 

Let  it  now  be  remembered  that  when  a  pound  of 
water  is  raised  one  degree  in  temperature  it  has  been 
endowed  with  778  foot-pounds  of  energy.  As  the  specific 
heat  of  steam  is  one-half  that  of  water,  if  a  pound  of 
steam  be  raised  from  212°  to  300°  —  88°  it  has  had 

778  y  88 
— =  34,232  foot-pounds  of  working  power  added 

to  it.  The  working  power  of  steam  is  in  its  pressure, 
and  so  long  as  pressure  is  maintained  by  heat,  so  long 
can  work  be  done  with  it. 

The  Steam- Engine.  —  The  steam-engine  is  a  machine 
for  utilizing  steam-pressure.  The  pressure  of  the  steam 


108  NATURAL   PHILOSOPHY. 

upon  the  piston-head  in  the  cylinder  (Fig.  29)  depends 
upon  the  temperature  of  the  steam,  and  the  area  of  the 
piston-head  upon  which  the  steam  presses.  Thus,  if 
the  area  be  one  square  foot,  and  the  pressure  50  pounds 
per  square  inch,  the  total  pressure  will  be  50  X  144 
=  7200  pounds,  and  if  the  piston  moves  forward  a  foot 
with  that  pressure  it  does  7200  foot-pounds  of  work. 
In  order  to  find  the  work  the  engine  is  doing,  multiply 
the  area  of  the  piston  in  square  inches  by  the  pressure 
per  square  inch  shown  by  the  steam-gauge,  and  that 
product  by  the  number  of  feet  the  piston-head  travels 
per  second  or  per  minute. 
Thus,  if  the  length  of 
stroke  be  two  feet,  and 
if  the  balance  wheel  goes 
around  twice  a  second, 
the  piston  has  to  move 
backward  and  forward 

Km.  29. 

twice  in  that  time,  that  is, 

8  feet ;  and  if  the  area  of  piston  be  one  square  foot  and 
pressure  be  50  pounds  per  square  inch,  as  above,  then 
the  work  done  will  be  equal  to  7200  X  8  =  57,600 
foot-pounds  per  second,  which  equals  ^fj}0  =104 
horse-power. 

Because  the  steam  has  done  work  it  has  lost  tempera- 
ture proportional  to  the  work  done,  so  when  it  escapes 
from  the  engine  it  is  no  longer  as  hot  as  it  was  when  it 
came  from  the  boiler.  If  one  knows  the  temperature  of 
the  steam  as  it  enters  and  escapes  after  doing  its  work 
he  can  calculate  how  much  energy  it  lias  lost ;  but  this 
temperature  must  be  measured  on  the  absolute  scale. 


ON    HEAT.  109 

Suppose  an  engine  employs  steam  at  the  temperature 
of  260°,  and  that  it  escapes  into  the  air  at  a  tempera- 
ture of  215°;  it  has  lost  260°  —  215°  =  45°.  But  260° 
Fahrenheit  — 260°  +  459°  =  719°  absolute  temperature, 
and  215°F.  =  215  +  459  =  674°  absolute. 

The  temperature  at  the  start  being  719°,  and  at 
the  end  674°,  there  has  been  used  719  —  674  =  45°, 
which  is  only  a  little  more  than  6^  of  the  whole 
amount. 

If  t  represents  the  absolute  temperature  of  the  steam 
in  the  boiler,  and  t1  the  absolute  temperature  on  its 
escape  from  the  cylinder  of  a  steam-engine  after  it  has 

t £] 

done  its  work,  then  —     —  represents  the  efficiency.  This 

may  be  applied  to  any  kind  of  heat  engine. 

The  ratio  of  the  amount  of  energy  used  to  the  whole 
amount  supplied  is  called  the  efficiency. 

If  the  steam-engine  could  be  worked  down  to  the 
temperature  of  32°,  its  efficiency  would  be  increased 

719  —  491      228 
very  much,  for,  as  before, — ==——=3256,  and 

I   J-  *J  I   A  «7 

if  it  could  l>e  worked  down  to  absolute  zero,  the  effi- 
ciency would  l>e  100y6. 

As  steam  condenses  to  water  at  212°  its  available 
gaseous  pressure  is  gone,  hence  its  serviceability  in- 
( •  reuses  as  its  temperature  increases  above  that.  It  has 
not  been  found  practicable  to  use  steam  at  a  higher 
temperature  than  about  400°,  859  absolute,  as  the  oils 
needed  for  lubricating  are  decomposed  by  higher  tem- 
peratures, and  the  valves  leak.  At  that  temperature 
the  pressure  is  not  far  from  250  pounds  per  square  incli. 


110  NATURAL   PHILOSOPHY. 

If  an  engine  be  worked  between  the  limits  of  400° 
and  212°  (859  —  671=188  absolute  temperature)  its 

188 
efficiency  would  be  the  highest,   namely  —-  =  22^. 

8o9 

This  shows  that  our  present  steam-engines  are  not 
economical,  for  under  the  best  conditions  three-fourths 
of  the  energy  supplied  to  them  is  wasted. 

The  energy  for  making  steam  is  supplied  by  the  fuel, 
—  coal,  wood,  gas,  or  oil.  Suppose  it  be  coal,  one 
pound  of  which  when  burned  can  raise  the  tempera- 
ture of  12,000  pounds  of  water  one  degree.  One  pound, 
then,  has  12,000  X  778  =  9,336,000  foot-pounds  of  work 
possible  in  it.  A  horae-power  is  550  foot-pounds  per 
second,  or  550  X  3600  =  1,980,000  per  hour;  hence  one 
pound  of  coal  has  energy  enough  to  maintain  a  horse- 

9,336,000 

power  — —         —  =  4.7  hours,  if  it  could  be  all  utilized. 
1,980,000 

As  a  matter  of  fact  it  takes  about  two  pounds  of  coal  to 
maintain  a  horse-power  for  an  hour  in  good  engines, 
and  two  or  three  times  as  much  in  the  poorer  ones. 
Two  pounds  of  coal  have  2  X  9,336,000=18,672,000  foot- 
pounds' work.  In  the  engine  they  give  but  1,980,000, 

1  980  000 

hence  -  ]       '     ^K  =  10  5&»    which   represents   the    real 
18,572,000 

efficiency  of  a  good  steam-engine. 

The  steam  plant,  as  it  is  called,  consists  of  a  fnr)i<t<'<- 
for  combustion,  a  boiler  for  converting  heat  energy  into 
mechanical  pressure,  the  pipes  for  directing  the  pressure 
to  the  engine  where  the  steam-pressure  is  transferred  to 
the  moving  piston,  and  then  to  the  wheels,  from  which 
it  is  transferred  by  belts  or  gears  to  other  machinery: 


ON    HEAT.  Ill 

We  start  with  chemical  energy  in  cold  fuel,  which  is 
transformed  into  heat  in  the  furnace ;  the  heat  is  trans- 
ferred to  the  water,  and  changes  it  into  a  gas  with  free- 
path  motions  and  pressure  measurable  in  pounds  per 
square  inch.  The  pressure  on  the  moving  piston  gives 
work,  and  its  rate  is  measured  in  horse-power.  From 
the  beginning  to  the  end  of  the  process  the  machineiy, 
of  whatever  kind  it  is,  does  nothing  but  change  the 
( -in -rgy  from  one  kind  or  direction  to  another;  and  no 
more  energy  can  be  obtained  from  the  engine  than  goes 
in  at  the  furnace.  This,  perhaps  one  would  say,  was 
obvious  enough,  yet  there  are  not  a  few  persons  who 
imagine  that  mechanism  can  of  itself  produce  energy. 
This  is  what  is  implied  in  all  attempts  at  what  is  called 
perpetual  motion.  The  effort  is  to  make  some  machine 
do  work  which  is  not  supplied  with  energy  from  some 
external  source.  No  one  has  succeeded  hitherto,  and 
we  know  why  not.  A  machine  transforms  or  transfers 
energy  supplied  to  it,  nothing  more. 

Nature  of  Heat.  —  From  all  that  has  been  said  one 
may  conclude  that  heat  phenomena  are  due  to  the 
vibratory  motions  of  atoms  and  molecules  —  not  transla- 
tory  in  either  long  or  short  paths.  Translatory  motions 
are  the  results  of  heat  motions,  for  a  molecule  might 
have  any  assignable  temperature,  and  yet  remain  in  the 
same  place,  if  not  otherwise  disturbed  (p.  72).  Also 
that  the  energy  of  heat  is  only  energy  in  this  atomic 
and  molecular  form  of  vibration.  When  this  form  or 
kind  of  motion  is  changed  into  another  in  any  way,  it  is 
no  longer  heat.  When  one  considers  the  characteristic 


112  NATURAL    PHILOSOPHY. 

of  heat,  it  is  proper  to  consider  it  as  a  mode  of  motion. 
When  one  considers  what  and  how  much  work  a 
definite  amount  can  do,  it  is  proper  to  consider  it  as  a 
mode  of  energy.  When  one  would  think  out  what 
happens  in  a  mechanical  way  in  heat  phenomena,  one 
must  think  of  modes  of  motion,  —  of  the  kinds  of 
motion  that  precede  the  appearance  of  heat  as  well  as 
those  into  which  the  heat  loses  its  identity.  The 
word  heat  itself  gives  no  clue  to  its  nature  or  mode  of 
operation. 

QUESTIONS. 

1.  How  many  heat  units  are  there  in  ten  pounds  of  each  of 
the  following  substances  :  coal,  wood,  kerosene  oil,  fat? 

2.  If  ten  per  cent  of  the  coal  were  ash  or  stone,  how  many 
heat  units  would  there  be  in  100  pounds? 

3.  How  many  foot-pounds  of  work  are  the  equivalent  of  one 
ounce  of  pure  coal  ? 

4.  If  the  work-power  of  one  pound  of  pure  coal  were  applied 
to  raising  itself,  how  high  would  it  be  raised  ? 

5.  What  weight  of  coal  would  be   necessary  to  raise  yourself 
ten  feet  high,  if  all  its  working  power  could  be  utili/ed? 

6.  If  only  ten  per  cent  of  its  power  could  be  thus  used,  how 
much  more  would  be  needed  to  do  the  same  work? 

7.  If  a  steam-engine  does  2,000,000  foot-pounds  of  work  in 
an  hour,  what  is  its  horse-power? 

8.  If  a  steam-engine  utilizes  but  6  per  cent  of  the  working 
power  of  the  coal  and  burns  a  ton  an  hour,  what  horse-power  has 
the  engine? 

9.  A  large  ocean  steamer  uses  five  hundred  tons  of  coal  a  day. 
If  it  takes  two  pounds  per  hour  per  horse-power,  what  is  the  horse- 
power of  the  engine  ? 

10.    If  it  takes  two  pounds  of  coal  to  maintain  a  horse-power 
for  an  hour  in  a  given  steam-engine,  what  is  the  <  /1ici<  n<\//  of  the 


ON    HEAT.  113 

engine,  that  is,  what  per  cent  of  the  whole  energy  of  the  coal  is 
made  serviceable? 

11.  How   many  degrees  above   the    freezing   point   will    100 
pounds  of  water  be  heated  by  all  the  heat  developed  by  burning 
one  pound  of  pure  coal  ? 

12.  How  many  degrees  will  the  same  amount  be  heated  by 
burning  one  pound  of  wood?     Also  by  a  pound  of  coal  oil? 

13.  If  it  takes  thirty  times  as  much  heat  to  raise  the  tempera- 
ture of  a  pound  of  water  one  degree  as  it  does  to  raise  a  pound  of 
lead  one  degree,  how  many  degrees  will  a  pound  of  lead  be  heated 
by  the  work  of  778  foot-pounds? 

14.  If  the  specific  heat  of  iron  be  .11,  how  many  degrees  will 
a  pound  of  iron  be  heated  by  the  amount  of  work  that  will  heat 
a  pound  of  water  one  degree  ? 

1").    A  bullet  weighing  one  ounce  strikes   a  target  with  the 
velocity  of  1000  feet  a  second ; 

(1)  How  many  foot-pounds  of  energy  does  it  have  ?  - — =energy. 

(2)  If  the  bullet  were  made  of  water,  how  many  degrees  would 
it  be  warmed  by  the  impact? 

(3)  If  the  bullet  were  made  of  lead,  specific  heat  =  ^,  and 
half  the  work  were  spent  upon  the  target,  how  much  would  the 
bullet  be  heated? 

(I)  Tf  the  bullet  were  iron,  how  many  degrees  would  it  be 
heated  under  the  same  conditions? 


CHAPTER   IX. 

ELECTRICITY  AND  MAGNETISM. 
ELECTRICITY. 

I.  Origin  of  Electricity.  —  If  a  strip  of  zinc  be  put 
into  some  water  in  a  tumbler  or  other  convenient  vessel, 
nothing  appears  to  happen  to  it.  If  a  little  acid  of  any 
kind  be  added  to  the  water,  bubbles  will  collect  upon  the 
zinc,  indicating  that  the  zinc  is  being  dissolved  slowly. 
Now  let  a  carbon  rod  such  as  is  used  for  the  arc  light  be 
put  into  the  same  liquid,  but  not  so  as  to  touch  the  zinc 
—  the  carbon  is  not  acted  upon  apparently,  and  the  zinc 
is  dissolved  slowly  as  before.  Let  the  carbon  lean  so  as 
to  touch  the  zinc,  and  at  once  the  zinc  shows  signs  of 
increased  activity,  —  the  bubbles  collect  fast  on  the 
carbon,  break  away  from  it,  and  rise  to  the  surface.  This 
action  stops  when  the  zinc  and  carbon  are  separated. 
If  a  wire  be  connected  to  the  carbon  rod  and  the  other 
end  of  it  be  touched  to  the  zinc,  the  action  is  again  set 
up ;  the  zinc  is  more  rapidly  dissolved  when  it  is  in  con- 
nection with  the  carbon  either  directly  or  by  means  of 
the  wire.  This  indicates  that  in  some  way  the  carbon 
affects  the  zinc  through  the  wire.  It  makes  no  differ- 
ence what  the  kind  of  wire  may  be.  Copper  wire  is 
more  generally  used  because  it  is  abundant,  easily  bent 
or  twisted,  and  is  otherwise  well  adapted  to  electrical 
work;  but  iron,  German  silver,  platinum,  and  other 
metals  show  the  same  phenomena,  indicating  some  sort 


ELECTRICITY    AND    MAGNETISM.  115 

of  physical  action  going  through  the  wire.  The  action 
in  the  solution  is  partly  chemical  and  partly  some  other 
kind,  which  has  the  name  electrical  to  distinguish  it 
from  the  first;  and  the  action  that  takes  place  in  the 
wire  is  called  an  electrical  current. 

That  something  goes  on  in  the  wire  is  shown  in  other 
ways  also.  For  instance,  if  the  wire  conveying  such 
electrical  current  be  held  close  over  a  common  compass 
needle  and  parallel  with  it  (Fig.  30),  the  needle  will  be 
deflected  one  way  or  the  other,  depending  upon  which 
end  of  the  wire  is  connected  with  the  zinc,  for  if  the 


ends  of  the  wires  be  changed  from  one  to  the  other 
element  in  the  solution  the  current  will  be  reversed  in 
the  wire  and  the  needle  will  be. deflected  in  the  opposite 
direction.  For  experimental  purposes  such  an  electric 
cell  as  the  above  will  not  answer  as  well  as  some  of 
those  found  in  the  market,  but  they  differ  only  in 
the  (quantity  of  current  given,  and  we  may  use 
any  of  the  numerous  forms  of  Leclanche  battery  cells 
in  place  of  the  arrangement  described  above.  The 
Leclanche  (Fig.  31)  consists  of  zinc  and  carbon  in  a 
solution  of  sal  ammoniac,  and,  as  before,  the  zinc  is 


116 


NATURAL    PHILOSOPHY. 


FIG.  31. 
Leclanche  Cell. 


dissolved,  the  carbon  is  not,  and  a  current  of  electricity 
traverses  the  wire  when  it  connects  the  two  substances. 
It  has  been  found  needful  for  convenience  to  assume 
that  the  current  in  this  wire  has 
always  a  certain  direction  which 
depends  upon  the  carbon  element. 
yoiny  out  from  that,  and  one  may 
with  a*  compass  needle  quickly  de- 
termine in  which  direction  the  cur- 
rent is  going  in  the  wire.  If  one 
bring  the  wire  down  over  the  needle 
and  parallel  with  it,  as  in  Fig.  30, 
if  the  current  be  goiny  north,  the 
north  end  will  turn  to  the  west.  If 
going  south,  the  south  end  of-  the 
needle  will  turn  to  the  west.  Remember  this  for  its 
convenience. 

A  compass  needle  with  a  coil  of  wire  around  it  or 
under  it  through  which  a  current  of  electricity  may 
be  sent  is  called  a  galva- 
nometer (Fig.  32). 

If  it  be  a  delicate  one  the 
needle  will  move  when  the 
ends  of  a  copper  and  an  iron 
wire  connected  with  it  are 
dipped  into  a  drop  of  salt  or 
acid  water.  The  combina- 
tion forms  a  small  battery. 

Another  way  of  generat- 
ing electricity  is  to  take  an 
ordinary  magnet,  either  a  straight  bar  or  of  horse-shoe 


ELECTRICITY    AND    MAGNETISM.  117 

form,  and  wind  about  one  of  its  ends  a  dozen  turns  of 
copper  wire  so  loosely  that  the  coil  Avill  slip  off  and  on 
easily.  Then  if  the  ends  from  this  coil  be  connected 
to  the  galvanometer  (Fig.  33)  and  the  coil  be  moved 
back  and  forth  over  either  end 
of  the  magnet  the  needle  will 
move  this  way  and  that,  de- 
pending upon  which  way  the 
coil  moves  and  also  upon 
which  pole  is  used.  But  the 
galvanometer  must  be  so  far 
from  the  magnet  that  the 
movements  of  the  latter  will 
not  appreciably  disturb  it. 

The  effects  upon  the  needle  are  the  same  as  was 
noticed  with  the  chemical  or  galvanic  cell,  indicating 
that  a  similar  condition  exists  in  the  connecting  wire, 
that  is,  that  a  current  of  electricity  is  going  through 
the  wire.  If,  instead  of  moving  the  coil  back  and  forth, 
it  be  held  still,  and  a  piece  of  iron  or  the  keeper  of  the 
magnet,  as  the  armature  of  it  is  called,  be  pulled  off  its 
poles  and  put  on  again,  the  effects  are  the  same;  the 
direction  of  the  needle  is  reversed  when  the  action  is 
reversed,  showing  the  existence  of  opposite  currents. 

In  one  important  point  this  way  of  generating  an 
electric  current  differs  from  the  chemical.  In  the  latter, 
the  current  continues  as  long  as  the  wires  are  connected 
to  the  battery.  In  the  former,  the  current  continues 
only  as  long  as  there  is  some  kind  of  movement  of  the 
coils  at  the  ends  of  the  magnet;  when  the  movement 
stops  the  current  stops,  although  the  wires  may  be  in 


118 


NATURAL    PHILOSOPHY. 


connection.     The  first  is  called  a  continuous  current, 

the  second  an  intermittent  current. 

A  third  way  of  generating  an  electric  current  is  to 

have  two  wires  of  different  metals,  as  iron  and  copper, 

twisted  together  at 
one  end  (Fig.  34),  and 
heated  at  this  junction. 

A  continuous   current 
FIG.  34.  ,  i  ,    , ,  , 

through  the  galvanom- 
eter is  furnished  by  this  means,  but  with  wires  as 
described  it  is  not  as  ^strong  as  the  current  from  the 
cell.  If  such  elements  as  antimony  and  bismuth  be 
taken  in  short  bars  and  soldered  together  at  their 
alternate  ends,  there  is  formed  what  is  called  a  thermo 
pile,  which  may  be  used  for  some  purposes.  A  still 
better  one  is  made  by  using 
bars  half  an  inch  thick  and 
two  inches  long,  of  an  alloy 
of  antimony  and  zinc  for 
one  metal  and  German  sil- 
ver for  the  other,  all  ar- 
ranged in  a  circular  form, 
as  shown  in  Fig.  35,  so  that 
a  gas  jet  can  heat  the  ends 
of  the  elements ;  twenty 
such  elements  in  one  gas 
jet  are  better  than  the  chemical  cell  described.  There 
are  still  other  sources  of  electrical  currents,  such  as 
electrical  eels  and  fishes,  atmospheric  conditions  which 
produce  lightning,  and  physiological  conditions,  for 
every  time  a  muscle  is  contracted  a  slight  current  of 


FIG.  35. 


ELECTRICITY    AND    MAGNETISM.  119 

electricity  is  generated,  so  slight  that  the  most  delicate 
means  are  needful  to  observe  it. 

Let  us  now  return  to  these  various  sources  described, 
and  study  them  in  the  light  of  what  has  preceded  this 
chapter. 

When  the  magnetic  needle  turns  this  way  or  that  in 
response  to  the  electric  current  in  the  wire,  it  is  to  be 
remembered  that  such  movement  indicates  energy,  for 
it  would  not  move  unless  it  received  somehow  and  from 
somewhere  a  pressure  —  and  pressure  always  implies 
energy.  When  the  direction  of  the  current  is  changed 
the  pressure  upon  the  needle  changes  too,  and  as  this 
evidence  of  pressure  ceases  when  the  wire  is  discon- 
nected from  the  source  of  action,  one  must  look  to  see 
what  evidence  there  is  of  activity  in  these  various 
sources. 

1.  In  the  Galvanic  Cell.  The  solution  dissolves 
the  zinc ;  a  solid  is  made  to  assume  a  liquid  form, 
and,  as  was  pointed  out  on  p.  94,  wherever  there  is 
a  change  of  form  of  matter  from  solid  to  liquid  or 
gaseous,  there  is  always  an  exchange  of  energy. 
Zinc  has  more  atomic  energy  in  its  solid  form  than 
it  has  when  chemically  combined  with  anything,  the 
same  as  hydrogen  and  oxygen  have,  for  when  they 
unite  they  give  out  a  large  amount  of  energy  in  the 
form  of  heat.  When  combined  with  sulphuric  acid  and 
forming  zinc  sulphate  a  pound  of  it  yields  3000  heat 
units  of  energy,  but  when  this  process  takes  place  in  a 
galvanic  cell  this  energy  shoivs  itself  in  a  current  of  elec- 
iricity  instead  of  heat.  Hence,  in  a  galvanic  battery 
the  source  of  the  electric  current  is  the  molecular  energy 


120  NATURAL    PHILOSOPHY. 

of  the  zinc.  The  process  we  call  a  chemical  process, 
and  the  product  is  zinc  sulphate  and  an  electric  current, 
just  as  the  product  of  the  combination  of  oxygen  and 
hydrogen  is  water  and  heat. 

The  energy  of  the  electric  current  is  distributed 
through  the  wire,  and  it  possesses  a  property  of  push- 
ing or  pulling  upon  bodies  in  its  neighborhood  such  as 
heat  energy  does  not  have.  The  magnetic  needle  is 
peculiarly  sensitive  to  such  action  of  a  current,  and  it 
is,  therefore,  employed  as  an  indicator  or  measurer 
of  it. 

2.  In  the  Magnet  and  Coil.     When  the  magnet  and 
coil  of  wire  are  at  rest  —  that  is,  when  no  mechanical 
energy  is  employed  to  disturb  their  positions  —  there  is 
no    electrical    current    and   the    needle    remains    still. 
Unless  some  work  is  being  done  with  them,  there  is 
no  energy  to  be  spent  by  them  in  moving  the  needle. 
The  antecedent  to  the  current  in  this  case  is  mechanical 
energy,  as  chemical  energy  was  the  antecedent  in  the 
galvanic  cell.     The  product  is  the  same  but  the  factors 
are  different. 

3.  In  the   Thermo  Pile.     The   thermo  pile  may  be 
connected    to    the    wine    and    galvanometer,    but   the 
needle  is  as  idle  as  if   it  were  not  connected   until 
one    face  of   the    pile    is   heated ;    then   a  current   at 
once  results  and  the  needle  moves.     We  are  supposed 
to  have  a  definite  idea  of  heat  as  a  form  of  energy 
in   which   the   atoms  and  molecules  are  vibrating   at 
high  rates.     As  long  as  they  are  all  at  the  same  tem- 
perature they  are  in  equilibrium,  but  when  one  junction 
or  one  face  of  the  pile  is  heated  higher  than  the  other, 


ELECTRICITY    AND    MAGNETISM.  121 

energy  is  being  spent  at  different  rates  upon  the  two 
metals  that  form  the  couple.  Suppose  the  two  ele- 
ments of  the  thermo  pair  be  copper  and  iron ;  they  have 
different  atomic  weights  and,  therefore,  have  different 
vibratory  rates  and  different  rates  of  heat  conduction. 
Where  the  elements  are  in  contact,  and  are  heated,  their 
rates  are  quickened  and  they  mutually  interfere  with 
each  other.  If  the  other  ends  be  connected  with  a  wire 
so  as  to  form  a  circuit,  a  part  of  this  energy  shows  itself 
as  a  current  of  electricity,  and  the  rest  is  spent  in  rais- 
ing the  temperature  ;  if  the  wires  are  not  so  connected, 
the  whole  energy  is  spent  in  raising  the  temperature. 
As  in  the  other  two  sources  so  in  this,  energy  has  to  be 
spent  in  order  to  produce  the  current,  and  the  energy 
of  the  current  thus  derived  shows  itself  in  moving  the 
needle.  But  in  this  case  the  kind  of  energy  supplied 
is  unlike  either  of  the  others.  In  the  first  it  is  chemi- 
cal ;  in  the  second,  mechanical ;  in  the  third,  heat.  The 
product  is  the  same,  —  an  electric  current  in  each  circuit 
of  wire.  We  have  presented  a  curious  matter  for  con- 
sideration,—  like  results  from  seemingly  very  unlike 
causes. 

In  every  case  energy  of  some  kind  has  to  be  spent  in 
order  to  produce  electricity.  In  the  atmosphere,  when 
lightning  appears  —  which  is  a  transient  current  of  elec- 
tricity—  there  are  always  energy  transformations  going 
on.  The  wind  and  clouds  and  rain,  and  oftentime  hail, 
show  that  mechanical  causes,  heat  causes,  and  chemical 
causes  are  all  present. 


122  NATURAL  PHILOSOPHY. 

II.  Electrical  Terminology.  —  It  is  as  needful  to 
have  some  standards  for  use  in  electrical  phenomena  as 
it  is  in  mechanical  or  heat  phenomena.  In  mechanical 
measurements  we  use  pounds  and  feet  and  quarts  ;  in 
heat  we  use  heat  units  and  degrees  of  temperature.  If 
electricity  possesses  energy  it  has  pressure,  for,  as  ex- 
plained already,  whenever  energy  is  acting  there  is 
pressure,  and  the  unit  of  electrical  pressure  is  called  a 
volt,  just  as  the  unit  of  mechanical  pressure  is  called 
a  pound,  and  whatever  produces  electrical  pressure  is 
called  electro  motive  force. 

The  unit  of  electrical  current  is  called  an  ampere. 
It  means  the  rate  at  which  a  current  is  flowing  in  a 
wire  ;  very  much  as  the  rate  of  the  flow  of  water  from 
a  pipe  is  indicated  by  cubic  feet  per  second.  A  current 
of  one  ampere  will  in  one  second  give  a  quantity  of 
electricity  called  the  coulomb.  That  is,  a  coulomb  is  an 
ampere  per  second. 

The  size  of  a  conductor  as  well  as  its  quality  deter- 
mines how  much  electricity  can  go  through  it  in  a  given 
time,  very  much  as  the  size  of  a  pipe,  its  diameter,  length, 
and  smoothness  of  bore  will  determine  the  amount  of 
water  that  can  go  through  it  under  given  pressure. 
These  conditions  of  size  offer  a  resistance  to  the  flow  of 
water  called  friction  and  similar  conditions  of  hindrance 
to  the  flow  of  electricity  are  called  electrical  resistance, 
and  a  unit  of  such  resistance  is  called  an  ohm. 

The  unit  of  electrical  power  is  called  the  watt,  and 
represents  the  work  equivalent  of  a  current  of  one 
ampere  when  the  electric  pressure  is  one  volt. 


ELECTRICITY    AND    MAGNETISM.  123 

The  unit  of  electric  pressure  is  the  volt  ;         its  symbol  is  E. 

"        "     «        "        current  "    "    ampere  ;    "         "        "  C. 

"        "     "        "        resistance  "    "    ohm  ;         "         "        "  R. 

"        "     "        "        quantity  "    "    coulomb ;  "         "       "  Q. 

"        "     "        "        power  "    "    watt ;         "         "       "   W. 

These  factors  stand  in  certain  algebraic  relations  to 
each  other  which  may  be  thus  expressed  : 

electric  pressure 

* —  =  electric  current, 

electric  resistance 

or,  using  the  symbols  in  place  of  what  they  signify, 

f 

—  =  C,  which  is  known  as  Ohms  Law. 
It 

This  is  used  in  the  following  way. 

The  pressure  in  an  electric  circuit  is  10  volts,  its 
resistance  is  5  ohms  ;  what  current  is  flowing  in  it  ? 

10  volts 

—  =.  2  amperes. 
5  ohms 

Again,  a  current  of  8  amperes  flows  in  a  circuit  having 


124 


NATURAL    PHILOSOPHY. 


a  known  resistance  of  15  ohms,  what  is  the  pressure  ? 
RG—  E,  15  X  8  =  120  volts. 

If  any  two  of  these  factors  be  known  the  third  one 
may  be  computed  in  this  simple  way. 

In  order  to  measure  these  quantities  there  are  various 


FIG.  37. 

kinds  of  instruments.  Formerly  galvanometers  were 
almost  universally  used,  but  now  instruments  called 
voltmeters  (Fig.  36)  and  ammeters  (Fig.  37)  are  in  use 

which  indicate  di- 
rectly the  value  of 
the  pressure  or  the 
current,  just  as 
weighing  balances 
indicate  weight,  and 
thermometers  the 
temperature,  with- 
out  any  calculations. 
It  will  be  assumed  that  such  instruments  are  used 
in  the  indicated  experiments  which  follow  ;  also  that 


ELECTRICITY    AND    MAGNETISM. 


125 


there  are  boxes  containing  wires  of  known  resist- 
ance called  resistance  boxes  (Fig.  38)  with  conveniences 
for  connecting  wires,  and  for  changing  the  resistance. 
Such  wires  are  only  measured  lengths  of  German  silver 
wire  which  have  resistances  so  arranged  that  one  can 
use  any  number  of  ohms  from  one  to  the  upper  limit 
of  the  particular  box. 


Electrical  Measurements. 

I.  Electric  Pressure.  —  To  determine  voltage  or 
pressure.  Suppose  there  be  for  study  two  Leclanche 
cells. 

(1)  Connect  one  of  the  cells  to  the  voltmeter  with 
wires  two  or  three  feet  long  that  have  been  coiled  up 
by  winding  them  around  a  convenient  rod  to  keep  them 
from  sprawling  (Fig.  39).    Be  sure  that  the  metallic  con- 
nections are  good,  and  also  that  each  wire 

is  connected  to  the  proper  terminal  on 
the  voltmeter.  The  pointer  will  indicate 
the  voltage  of  the  cell.  For  such  a  cell 
as  the  above  the  pressure  will  probably 
be  somewhere  in  the  neighborhood  of 
1.4  volts.  See  whether  both  cells  have 
the  same  pressure. 

(2)  Couple    the    two    cells    together ; 
first,  the  zinc  of  one   to   the   carbon  of 

the  other,  and  the  remaining  carbon  and  zinc  to  the 
voltmeter,  and  note  whether  or  not  the  indicated 
voltage  is  the  sum  of  the  two.  Second,  couple  them 
zinc  to  zinc  and  carbon  to  carbon,  and  these  wires  to 


126  NATURAL   PHILOSOPHY. 

the  voltmeter.  If  there  be  other  kinds  of  cells,  such 
as  copper  sulphate  or  bichromate  of  potash,  they  may  be 
compared  with  the  others.  Ordinarily  copper-sulphate 
cells  have  1.1  volts  each,  and  bichromate-of-potash  cells 
about  2  volts.  The  voltmeter  is  so  constructed  that 
only  a  very  weak  current  goes  through  it,  and  only  a 
minute  quantity  of  electrical  energy  is  used. 

Now  let  a  short  piece  of  wire  be  touched  to  the 
terminals  of  the  battery  while  the  voltmeter  is  connected, 

and  observe  the  latter  (Fig.  40).     When 
v  ^        the  wire  first  touches,  the  needle  falls  a 

good  deal  and  continues  to  fall  while 

you  look  at  it. 


Actions  of  the  Cells.  —  The  explana- 
tion of  this  will  be  seen  in  making  a  cell 
like  the  first  one  mentioned  (p.  114)  of 
zinc  and  carbon  in  a  solution  of  dilute 
sulphuric  acid.  The  bubbles  will  collect 
upon  the  carbon  rod  and  nearly  cover  it,  thus  keeping 
the  liquid  from  touching  it.  The  bubbles  are  hydrogen 
gas  there  set  free  by  the  decomposition  of  water.  Of 
course,  if  the  liquid  cannot  touch  the  carbon  the  latter 
may  as  well  be  out  in  the  air ;  the  current  is  nearly 
stopped,  and  the  electric  pressure  is  reduced  as  indicated. 
This  collecting  of  the  gas  upon  the  carbon  is  called 
battery  polarization.  The  zinc  first  decomposes  the 
water  and  unites  with  the  oxygen  forming  zinc  oxide, 
which  then  combines  with  the  sulphuric  acid  forming 
zinc  sulphate.  In  chemical  symbols  it  is  like  this  : 

Zn  +  H2O  +  S03  =  ZnO  +  S03  -f  Ha. 


ELECTRICITY    AND    MAGNETISM.  127 

The  ZnO  combining  with  SO3  becomes  ZnSO4,  and 
that  leaves  the  hydrogen  free,  but  here  is  the  most 
singular  phenomenon  in  the  whole  process,  —  none  of 
the  hydrogen  appears  at  the  zinc  surface  when  the 
water  is  decomposed  ;  it  all  is  at  the  carbon  plate.  To 
understand  this  it  would  be  needful  to  look  down 
among  the  molecules  with  the  imaginative  eye  to  see 
what  must  be  going  on.  As  the  zinc  is  capable  of  com- 
bining with  oxygen  in  definite  proportion,  there  is  what 
is  called  chemical  attraction  between  the  two.  When 
the  zinc  is  immersed  in  the  solution  the  attraction  is 
not  quite  strong  enough  to  decompose  the  water,  as  a 
piece  of  potassium  will  do,  but  the  attraction  is  there, 
and  every  water  molecule  adjacent  to  the  zinc  is  swung 
round  so  that  its  oxygen  face  fronts  the  zinc.  It  can 
do  this,  for,  as  has  been  pointed  out,  there  is  no  friction 
among  water  molecules  ;  they  are  free  to  turn  about  in 
any  direction.  So  the  oxygen  sides  are  towards  the 
zinc  and,  of  course,  the  hydrogen  sides  are  away  from  it. 
The  carbon  does  not  act  upon  the  water,  it  will  not 
decompose  it  except  at  a  red 
heat ;  and  when  a  current  of 
electricity  flows,  as  it  always  ~* 
will  in  such  a  cell,  it  goes 
from  the  zinc  to  the  carbon, 

and  there  is  an  interchange  of  atoms  among  the  mole- 
cules along  the  whole  line.  Fig.  41  shows  this,  where 
the  water  molecules  are  represented  by  circles,  one 
al)ove  the  other,  the  hydrogen  circles  having  lines 
drawn  across  them,  the  lower  circles  being  oxygen. 
If  the  lower  left-hand  oxygen  atom  1  be  taken  away, 


128  NATURAL   PHILOSOPHY. 

the  hydrogen  with  which  it  was  combined  at  once  com- 
bines with  2,  the  oxygen  of  the  next  adjacent  molecule, 
and  its  hydrogen  to  the  next,  until  the  last  at  the  sur- 
face of  the  carbon  where  there  is  no  longer  any  oxygen 
for  hydrogen  of  7  to  combine  with,  and  therefore  it  is 
set  free.  There  has  been  decomposition  and  recom- 
position  of  every  molecule  along  the  whole  line. 

This  is  the  way  the  hydrogen  gets  to  the  carbon  in 
the  cell,  and  as  it  sticks  there  it  presently  brings  the 
cell  to  a  standstill.  To  prevent  this  various  means  are 
employed.  In  the  Leclanche  cell  the  carbon  is  mixed 
with  binoxide  of  manganese,  the  whole  is  then  pressed 
into  sticks  or  cylinders  and  baked.  The  manganese 
gives  up  freely  some  of  its  oxygen  to  the  hydrogen 
just  set  free,  and  water  is  again  formed  at  the  carbon 
surface.  This  gets  rid  of  the  gas,  but  the  solution 
left  is  so  weakened  after  a  time 
that  the  cell  is  spoiled.  Another 
way  is  by  putting  the  carbon 
into  a  porous  jar  containing 
nitric  acid  or  chromic  acid,  and 
setting  this  down  into  the  solu- 
tion with  the  zinc.  This  answers 
very  well  while  the  strong  acid 
lasts.  When  the  zinc  is  put  into 
dilute  sulphuric  acid  such  a  cell 
is  called  the  Bunsen  cell  (Fig. 
42).  It  has  a  pressure  of  about 
1 .9.  If  the  zinc  be  put  into  sal 

ammoniac,  instead  of  into  sulphuric  acid  as  proposed 
by  the  author,  the  pressure  is  2.2  volts.  Such  batteries 


ELECTRICITY    AND    MAGNETISM.  129 

are  called  two-fluid  cells,  and  the  second  liquid  em- 
ployed, viz.,  the  one  in  which  the  carbon  stands,  is 
called  a  depolarizer,  as  its  chief  function  is  to  prevent 
the  collection  of  hydrogen  gas  on  the  plate  immersed 
in  it. 

While  the  cell  being  examined  is  connected  with  the 
voltmeter,  slowly  raise  the  elements  out  of  the  liquid, 
observing  whether  there  is  any  change  in  the  voltage. 
It  will  be  found  that  the  extent  of  surface  exposed  to 
the  liquid  does  not  affect  the  pressure.  That  is,  the 
pressure  depends  upon  the  character  of  the  chemical 
work  and  not  its  amount.  A  small  cell  of  a  given  kind 
has  the  same  electric  pressure  as  one  made  ten  or  a 
hundred  times  larger.  This  may  remind  one  of  the 
pressure  of  water  per  square  inch,  which  depends  upon 
the  depth  of  the  water  rather  than  its  quantity. 

II.  Measure  of  the  Current. —  Let  now  the  ammeter 
A  be  put  in  the  circuit  with  the  batteiy  B  and  the  set 
of  resistance  coils  E  (Fig.  43). 
As  the  resistances  are  varied  the 
current  becomes  more  or  less, 
according  to  Ohm's  Law.  Sup- 
pose that  tin-  ammeter  indicates 
one-half  an  ampere  ;  the  voltage 
being  known,  suppose  it  1x3 1.4  ; 

then  according  to  Ohm's  Law  —  =  R,  -^-  =  2.8  ohms. 

6  .5 

This  resistance  is  made  up  of  tin-  resistances  of  the  bat- 
tery itself,  of  the  connecting  \viivs,  of  the  ammeter,  and 
the  resistance  in  the,  box  of  coils.  Usually  the  resistance 


130  NATURAL   PHILOSOPHY. 

of  the  ammeter  is  so  small  it  need  not  be  reckoned,  and 
the  same  with  the  connecting  wires,  so  the  R  is  made  up 
of  the  resistance  in  the  battery  and  in  the  coils.  That 
in  the  coils  can  be  read,  suppose  it  be  2  ohms.  Then  as 
the  total  resistance  is  2.8  ohms,  the  resistance  of  the 
battery  itself  will  be  .8  ohms.  This  resistance  of  the 
battery  cell  depends  upon  the  size  of  the  cell.  Raise 
the  elements  out  of  the  solution  slowly  while  the 
motion  of  the  ammeter  needle  is  watched ;  the  current 
becomes  less  and  less  as  the  immersed  surface  is 
lessened.  If  the  surface  in  contact  with  the  solution 
be  thus  reduced  one-half,  the  resistance  of  the  cell,  if 
measured  as  above,  will  be  found  to  be  1.6  ohms. 

III.  Measure  of  Resistance.  —  The  resistance  of  a 
length  of  wire  of  any  kind  may  be  measured  by  putting 
it  in  circuit  with  the  ammeter  and  a  battery  cell,  and 
noting  the  current  that  is  indicated.     Now  replace  the 
wire  with  the  resistance  box  and  see  what  number  of 
ohms  must  be  put  into  the  circuit  in  order  to  give  the 
same  reading  upon  the  ammeter.    This  number  of  ohms 
will  be  the  resistance  of  the  wire  being  measured.    This 
is  called  measuring  resistance  by  substitution.     There 
are  other  ways  of  measuring  it  with  a  higher  degree  of 
precision  than  this,  but  this  way  seems  to  show  the 
nature  of  the  process,  and  still  better,  it  shows  that 
electrical  phenomena  are  as  subject  to  law  as  mechanical 
or  heat  phenomena,  and  may  be  as  definitely  known. 

IV.  Energy  of  a  Battery.  —  The  working  power  of 
water  is  measured  by  multiplying  the  water  pressure 
by  the  amount  of  water  that  flows  per  second  ;  and  in 


ELECTRICITY   AND   MAGNETISM.  131 

like  manner  the  working  power  of  electricity  may  be 
found  by  multiplying  its  pressure  in  volts  by  its  current 
in  amperes,  that  is,  EC,  and  this  product  is  called  watts, 
of  which  746  equal  a  horse-power,  and  each  horse-power 
equals  550  foot-pounds  per  second  (p.  40).  If  a  battery 
has  one  volt  pressure  and  gives  one  ampere  current, 
its  energy  is  1  X  1  =  1  watt  =  -y-!g-  of  a  horse-power, 
w  \ ,.  of  550  =  .75  of  a  foot-pound  per  second.  This  is 
a  small  quantity.  How  may  it  be  increased  ? 

Suppose  the  cell  has  one  volt  pressure  and  a  resistance 
of  half  an  ohm,  and  the  external  wire  through  which 
the  current  has  to  flow  has  half  an  ohm,  the  whole  may 

be  represented  thus :  — =  1  ampere.     If  we  make 

.5  — j—  .5 

the  cell  larger  we  make  its  resistance  less,  but  that  does 
not  change  its  pressure.  Suppose  it  be  made  five  times 
as  large,  the  resistance  of  the  cell  will  be  reduced  to 

£  X  3y  =  y  o  °f  an  ohm,  and  the  current  will  be  - 

.1  -\-.b 

=  1.06  amperes,  and  the  working  power  will  be  1  X  1.66 
=  1.66  watts,  or  1.24  foot-pounds  per  second. 

Suppose  the  pressure  of  the  cell  be  increased  by 
employing  different  chemicals.  This  may  be  done  so  as 
to  make  it  equal  two  volts.  With  the  other  conditions 
as  before  this  will  double  the  working  power,  for  now 
there  will  be  2x1.66  =  3.32  watts.  It  is  not  at 
present  practicable  to  have  much  more  than  two  volts 
to  a  cell,  neither  is  it  practicable  to  have  the  resist- 
ance of  a  cell  less  than  .1  of  an  ohm ;  so  the  above  shows 
about  the  maximum  work  to  be  got  out  of  one  cell  of 
ordinary  size. 


132  NATURAL   PHILOSOPHY. 

If  one  wishes  to  find  how  many  cells  are  needed  for  a 
horse-power  he  must  remember  that  watts  is  the  product 
of  volts  and  amperes  ;  746  watts  are  required.  If  the 
current  be  10  amperes  there  must  be  74.6  volts,  and  if 

7  A.   f\ 

each  cell  has  two  volts,  — ~  =  38  cells  —  as  there  cannot 

be  half  a  cell.  If  a  current  of  20  amperes  be  used  the 
number  of  cells  will  be  one-half,  but  their  size  will 
necessarily  be  greater,  for  it  will  be  remembered  that 
the  current  of  a  cell  depends  upon  its  size.  One 
can  see  from  the  above  why  galvanic  batteries  have 
not  been  used  for  many  purposes  even  when  only  a 
small  amount  of  power  is  required.  Another  reason 
that  they  are  not  available  for  such  purpose  is  the 
necessity  for  frequent  renewal  of  the  materials,  which, 
without  the  greatest  painstaking,  is  sure  "  to  make  a 
mess." 

Again,  zinc  has  the  same  function  in  a  battery  that 
coal  has  in  a  steam-engine.  Zinc  has  3000  heat  units 
value  per  pound,  while  pure  coal  has  14,500. 

778  x     3000  =    2,334,000  foot-pounds  for  the  pound  of  zinc. 
778  x  14,500  =  11,281,000          «  «     «         «      «   coal. 

The  coal  has  nearly  five  times  as  much  as  the  zinc.  Ziric 
is  worth  about  100  dollars  a  ton,  while  coal  can  be  had 
for  3  dollars  a  ton.  A  given  amount  of  power  got  from 
zinc  costs  over  a  hundred  and  fifty  times  as  much  as  it 
does  from  coal.  It  should  be  kept  in  mind  that  the 
substances  used  in  batteries  have  definite  working  power 
per  pound  and  that  no  kind  of  machinery  or  combi- 
nations can  increase  it  but  may  greatly  waste  it. 


ELECTRICITY    AND    MAGNETISM.  133 

V.  Electrical  Conductivity.  —  If  one  take  a  number 
of  different  kinds  of  wire  such  as  silver,  copper,  iron, 
German  silver,  or  others,  all  of  the  same  length  and 
thickness,  and  connect  them  one  at  a  time  to  a  battery 
or  other  source  of  electricity,  having  an  ammeter  in 
the  circuit,  he  will  see  that  the  current  will  not  be  the 
same  for  any  two.  For  silver  the  current  will  be  the 
greatest,  and  it  will  be  much  less  for  German  silver. 
The  differences  are  due  to  the  degrees  of  conductivity 
of  the  substances  of  which  the  wires  are  made.  If,  for 
instance,  the  current  shown  by  the  ammeter  when  the 
silver  wire  was  tried  was  1  ampere,  while  for  iron  it 
was  but  .16  of  an  ampere,  and  for  German  silver  only 
.07  of  an  ampere,  it  would  show  that  silver  was  more 
than  six  times  as  good  a  conductor  for  electricity  as 
iron,  and  fourteen  times  as  good  as  German  silver.  In 
this  way  tables  of  conductivity  have  been  made  of  all 
the  metals  and  some  other  substances.  Here  are  a  few 
to  show  the  order  of  differences  in  them,  silver  being 
the  best. 

Silver.  Platinum. 

Copper.  Iron. 

Gold.  Lead. 

Aluminum.  German  silver. 

Zinc.  Mercury. 

Liquids  are  still  poorer  in  conductivity  than  any 
of  the  metals,  pure  water  being  very  nearly  a  non- 
conductor ;  a  drop  or  two  of  acid  or  a  pinch  of  salt 
in  a  pint  of  water  improves  its  conductivity  thousands 
of  times.  Bodies  whose  conductivity  is  veiy  small  are 


134  NATURAL   PHILOSOPHY. 

called  non-conductors  ;  thus  wood,  glass,  and  gases  are 
non-conductors.  Conductivity  and  resistance  are  com- 
plementary terms,  that  is,  one  increases  as  the  other 
diminishes.  This  is  sometimes  expressed  thus  :  con- 
ductivity varies  inversely  as  the  resistance.  For  most 
electrical  purposes  resistance  is  the  term  used  rather 
than  conductivity. 

These  differences  in  ability  to  conduct  electricity 
possessed  by  the  different  metals  depend  upon  their 
molecular  properties,  very  much  as  heat  conduction 
does.  Indeed,  bodies  that  are  good  conductors  of  one 
are  good  conductors  of  the  other. 

So  far  the  degree  of  conductivity  has  been  considered 
between  different  metals  when  they  are  of  the  same 
length  and  diameter. 

A  copper  wire  the  twenty-fifth  or  .04  of  an  inch,  in 
diameter,  and  150  feet  long  has  a  resistance  of  about 
one  ohm.  If  two  such  wires  were  stretched  together, 
the  two  could  conduct  twice  as  much  electricity  in  a 
given  time  as  one  could  do,  that  is,  the  conductivity  of 
the  two  is  twice  that  of  one.  If  both  these  were  made 
into  one  wire  of  the  same  length,  the  cross  section  of  it 
would  be  twice  as  great  as  the  cross  section  of  one.  If 
the  conductivity  be  doubled  the  resistance  is  reduced 
to  one-half  ;  hence  we  say  that  resistance  varies  in- 
versely as  the  cross  section  of  the  conductor.  When 
the  diameter  of  a  wire  is  doubled,  its  cross  section  is 
increased  four  times,  for  the  areas  of  circles  are  to  each 
other  as  the  squares  of  their  diameters.  Hence  a  wire 
150  feet  long  and  .08  of  an  inch  in  diameter  will  have 
a  resistance  of  only  one-fourth  of  an  ohm. 


ELECT1UC1TY    AND    MAGNETISM.  135 

Doubling  the  length  of  a  wire  doubles  its  resistance, 
so  we  say  the  resistance  of  a  wire  varies  as  its  length. 

Putting  these  facts  together  the  law  may  be  briefly 
stated  thus  : 

The  resistance  of  a  wire  varies  as  — ,  where  I  is  the 

a* 

length  and  d  its  diameter ;  also  it  varies  with  the  kind 

kl 
of  material,  k ;  altogether  it  varies  as  — . 

Tables  of  the  sizes  of  copper  and  iron  wires  and 
their  resistances  per  unit  of  length  or  weight  are  very 
common,  and  are  constantly  referred  to  in  electrical 
industries.  See  table,  page  312. 

The  resistance  of  a  common  telegraph  line  is  10  or 
more  ohms  to  the  mile,  that  of  an  arc-light  wire  about 
2  ohms  to  the  mile.  Hence  a  telegraph  line  100  miles 
long  will  have  a  resistance  of  a  1000  ohms  or  more  ; 
and  an  arc-light  circuit  20  miles  long  40  ohms.  These 
figures  are  for  the  wire  alone. 

All  electrical  devices  have  more  or  less  resistance. 
A  telegraph  relay  may  have  150  ohms'  resistance,  a 
sounder  10,  an  incandescent  lamp  100,  an  ocean  cable 
3000. 

The  conduction  of  electricity  requires  substantial 
contact  between  the  molecules  of  the  conductor,  in  the 
same  way  as  heat  does.  As  heat  separates  molecules,  it 
increases  the  resistance  of  a  conductor.  Conductivity 
increases  as  the  temperature  is  made  lower,  and  experi- 
ments indicate  that  at  absolute  zero  of  the  heat  scale 
none  of  the  metals  would  have  any  resistance,  they 
would  all  be  perfect  conductors. 


136  NATURAL   PHILOSOPHY. 

MAGNETISM. 

If  two  or  three  feet  of  insulated  wire  of  any  conve- 
nient size  be  wound  about  a  piece  of  iron,  as  a  large  nail 
or  bolt  or  plain  rod  (Fig.  44),  and  a  current  of  electricity 
be  sent  through  the  coil,  the  iron  becomes  a  magnet,  and 
other  pieces  of  iron  will  be  attracted  by  it  and  stick  to 
it  if  permitted.  As  soon  as  the  current  stops,  the  mag- 
netism mostly  dis- 

B  )  r~v~^^~v->-t_^-^v^^^^^  _  appears,  and  re  turns 

again  on  completing 
the  circuit.  If  the 
same  thing  be  done 

with  a  piece  of  hardened  steel,  the  latter  does  not  lose 
its  magnetism  on  opening  the  circuit,  —  it  has  become 
&  permanent  magnet.  It  is  more  convenient  to  study  the 
properties  of  magnetism  with  permanent  magnets  than 
with  temporary  or  electro-magnets,  as  they  are  called. 

Magnets  may  be  of  any  form  ;  ordinarily  they  are 
straight  bars  or  crooked  like  the  letter  U. 

Suppose  we  have  a  straight  steel  bar  magnet  six  or 
eight  inches  long,  and  an  ordinary  magnetic  needle, 
which  is  also  a  permanent  magnet,  suspended  so  as  to 
be  free  to  turn  towards  any  point  of  the  compass. 
When  the  bar  magnet  is  at  a  distance  the  needle  points 
towards  the  north,  and  the  end  that  points  north  is 
generally  marked  in  some  way  to  indicate  it.  If  the 
bar  magnet  be  brought  into  the  neighborhood  of  the 
needle  the  latter  will  turn  one  of  its  ends  toward  the 
bar  magnet.  If  an  attempt  be  made  to  bring  it  nearer 
the  other  end  of  the  needle  that  end  will  move  vigor- 


ELECTRICITY    AND   MAGNETISM. 


137 


ously  away,  and  can  be  brought  near  only  by  forcibly 
preventing  the  needle  from  turning  round.  To  de- 
scribe these  two  actions,  one  is  called  attraction,  the 
other  repulsion.  If  the  other  end  of  the  bar  U;  taken 
in  place  of  the  one  first  tried,  it  will  be  found  that  the 
end  of  the  needle  which  was  attracted  will  now  be 
repelled.  If  the  bar  be  suspended  by  a  string,  so  that 
it  also  may  be  free  to  turn,  it  too  will  point  to  the 
north  ;  and  if  the  end  which  is  towards  the  north  be 
marked  in  any  way  so  that  it  may  be  recognized,  and 
then  the  experiment  be  repeated,  it  will  be  found  that 

like  poles  of  a  may- 
net  repel  each  other, 
while  unlike  poles 
attract,  but  both 
poles  will  attract 
iron. 

Now  over  the  bar 
magnet  put  a  piece 
of  pasteboard  or  a 
pane  of  glass,  and 
upon  it  scatter 
loosely  some  iron 
filings  ;  jar  the 
glass  or  paper  a  lit- 
Fio  ^  tie,  and  the  filings 

will  be  seen  to  ar- 
range themselves  in  curved  lines  running  from  one 
pole  to  the  other  (Fig.  45).  When  thus  arranged  the 
pasteboard  or  glass  may  be  gently  raised  and  the  ar- 
ranged filings  may  be  taken  away.  If  the  paper  upon 


138  NATURAL    PHILOSOPHY. 

which  the  filings  are  strewn  be  first  covered  by  a  thin 
film  of  wax  or  paraffin,  it  may  afterwards  be  warmed 
without  disturbing  the  arrangement.  The  filings  will 
sink  through,  and  when  cool  again  will  be  fixed.  Such 
a  thing  is  called  a  magnetic  phantom. 

Theory  of  Magnetism.  The  study  of  this  phenome- 
non of  magnetite  arrangement  has  led  to  the  theory  of 
both  magnetic  and  electric  phenomena  which  we  must 
lu-iv  stop  to  consider. 

In  the  first  experiment  mentioned  above,  the  needle 
was  moved  this  way  or  that  by  the  mere  presence  of  the 
bar  magnet  without  one  touching  the  other,  or  even 
being  very  near  it.  This  shows  that  a  body  may  act 
upon  another  body  without  touching  it.  If  the  needle  be 
suspended  in  as  perfect  a  vacuum  as  can  be  made,  the 
action  is  not  stopped  in  the  least,  and  no  substance  has 
been  found  which,  if  interposed  between  a  magnet 
and  a  piece  of  iron  or  another  magnet,  will  prevent 
this  attraction  or  repulsion. 

As  no  one  has  been  able  to  imagine  how  one  body 
could  in  any  way  act  upon  another  body  not  in  contact 
with  it,  and  with  nothing  at  all  between  them,  it  is 
assumed  that  there  is  some  other  kind  of  substance' in 
space  than  ordinary  matter,  such  as  we  call  the  elements 
and  their  compounds.  It  is  called  the  ether.  It  is  be- 
lieved, (1)  that  it  quite  fills  space,  (2)  that  it  is  not  made 
up  of  atoms  like  ordinary  matter,  (3)  that  it  is  homo- 
geneous —  every  part  exactly  like  every  other  part,  (4) 
that  it  is  highly  elastic,  greatly  exceeding  steel  in  this 
particular,  (5)  that  it  is  frictionless,  so  bodies  can  freely 


ELECTRICITY    AND   MAGNETISM.  139 

move  through  it  and  not  lose  their  motion,  (6)  that  the 
whole  universe  of  matter,  suns,  planets,  and  stars  are 
swimming  in  it  —  indeed,  that  it  is  illimitable,  (7)  that 
it  possesses  an  immense  amount  of  energy  in  various 
forms,  and  (8)  that  it  is  capable  of  transmitting  energy 
of  certain  forms  with  enormous  velocity.  Light  is  one 
form  of  this  energy,  and  is  transmitted  by  this  ether  with 
the  velocity  of  186,000  miles  a  second.  The  ether  must 
extend  to  the  sun,  for  it  takes  eight  minutes  for  the 
sun's  light  to  get  to  the  earth,  a  distance  of  93,000000 
miles.  It  must  extend  to  the  fixed  stars,  the  nearest 
one  being  so  far  away  that  it  takes  3i  years  for  its 
light  to  reach  us ;  while  some  of  the  remote  stare 
are  so  distant  that  their  light  requires  thousands  of 
years,  traveling  at  the  above  rate,  to  get  to  us.  As 
the  light  is  a  kind  of  energy  and  will  do  work,  it  must 
be  energy  while  on  the  way,  and  energy  is  the  product 
of  something  into  a  rate  of  movement.  The  rate  we 
know ;  the  something  in  this  case  we  call  ether;  it  can- 
not be  matter. 

It  is  through  the  agency  of  this  space-filling  ether 
that  the  magnet  becomes  able  to  act  on  another  body. 
It  acts  first  upon  the  ether  about  it,  and  the  ether  reacts 
upon  the  second  body.  Experiments  have  shown  that 
this  action  upon  the  ether,  which  is  called  a  stress, 
extends  to  an  indefinite  distance  from  the  magnet  in 
every  direction,  only  becoming  weaker  as  the  distance 
increases.  The  bar  magnet  acts  strongly  upon  the 
needle  when  near  to  it,  at  the  distance  of  two  or  three 
feet  much  less ;  at  ten  feet  away  perhaps  one  could  not 
observe  that  the  needle  has  any  motion,  yet  if  the  latter 


140  NATURAL,   PHILOSOPHY. 

were  very  delicately  poised  it  would  move  appreciably. 
There  is  no  reason  to  doubt  that  the  magnet  affects  the 
whole  ether,  only  at  great  distances  it  is  too  weak  to 
be  observed.  The  space  about  a  maynet,  in  which  it  pro- 
duces a  stress,  is  called  a  magnetic  field. 

The  ether  stress  about  the  magnet  is  of  such  a  nature 
that  a  piece  of  iron  or  steel  or  another  magnet  in  the 
stress  is  simply  turned  into  a  new  position. 

Take  a  small  compass  and  move  it  about  the  larger 
magnet,  observing  the  position  the  small  needle  takes 
in  different  places.  Then  compare  these  positions  with 
the  lines  of  iron  filings  as  shown  on  the  phantom. 
They  are  the  same  in  direction.  The  filings  serve  to 
show  the  direction  of  the  stress  in  the  field.  Again, 
the  lines  all  start  from  one  of  the  ends  or  poles  and  go 
out  in  a  curved  line  towards  the  other  pole  to  reenter 
there,  so  that  each  line  appears  to  represent  a  circuit, 
part  in  the  magnet  itself,  the  rest  in  the  space  about  it. 
A  magnetic  circuit  consists  of  the  magnet  itself  and 
its  field;  the  magnet  may  have  any  form.  If  it  be 
shaped  like  the  letter  U,  the  field  is  close  to  the  poles. 
Place  a  U  magnet  under  the  plate  of  glass,  and  sprinkle 
iron  filings  upon  it.  They  will  arrange  themselves 
between  the  poles  in  straight  and  curved  lines,  and  the 
closer  the  poles  are  together,  the  denser  is  the  magnetic 
field. 

When  two  similar  magnets  have  their  similar  poles 
together,  their  fields  are  strengthened.  When  their 
opposite  poles  are  together,  they  cancel  each  other. 
This  can  be  seen  by  allowing  one  magnet  to  pick  up 
a  piece  of  iron,  as  a  nail.  Bring  down  slowly  another 


ELECTRICITY    AND    MAGNETISM.  141 

similar  pole  upon  the  pole  holding  the  nail ;  it  will  only 
stick  the  tighter  to  the  magnet.  Bring  down  the  other 
pole  to  the  same  place  and  the  nail  will  drop  off  easily, 
showing  that  the  magnetism  has  been  neutralized  like 
two  opposite  pressures  in.equilibrium.  Yet  each  mag- 
net has  lost  nothing,  for  when  separated  each  will 
attract  and  repel  as  well  as  ever.  The  reason  for  this 
apparent  loss  is  simply  that  the  field  has  been  destroyed 
because  all  the  stress  that  before  was  in  the  space  is 
now  in  the  opposite  magnet.  In  other  words,  iron  and 
steel  are  better  conductors  of  magnetic  stress  than  the 
air  is,  and  the  magnetism  goes  through  them  when  they 
are  present.  A  piece  of  iron  in  a  magnetic  field  absorbs 
the  stress  and  is  turned  by  it  into  a  new  position,  and 
every  piece  of  iron  that  has  absorbed  the  stress  is  itself 
a  magnet. 

Take  a  board  nail  and  some  tacks.  Unmagnetized, 
the  nail  will  not  pick  up  a  single  tack.  Slowly  bring 
down  towards  one  end  of  the  nail  one  pole  of  a  magnet. 
Before  the  magnet  has  touched  the  nail,  the  latter  will 
be  found  to  have  become  a  magnet,  and  a  tack  will 
stick  to  it.  If  now  it  be  permitted  to  touch  the  mag- 
netic pole,  other  tacks  will  stick  to  the  first  tack,  and  if 
the  magnet  be  a  strong  one,  half  .a  dozen  tacks  will 
hang  together  end  on  end,  even  when  the  magnet  is 
separated  slowly  from  the  nail.  This  action  by  which 
a  piece  of  iron  becomes  magnetic  by  being  in  a  magnetic 
field  is  called  magnetic  induction. 

Let  a  bar  magnet  of  any  convenient  size  be  put  into 
a  shallow  dish  and  covered  with  water  to  the  depth  of 
half  an  inch ;  scatter  a  few  iron  filings  upon  the  water, 


142  NATURAL   PHILOSOPHY. 

not  close  together.  They  will  not  sink,  but  will  arrange 
themselves  with  reference  to  the  magnet.  Now  let 
another  magnet  be  brought  over,  and  a  few  inches  from 
the  filings,  and  turned  so  as  to  present  first  one  pole 
then  the  other  to  them,  the  filings  will  be  seen  to  turn 
about  each  time  a  different  pole  is  presented  to  them, 
showing  that  the  particles  are  themselves  magnets,  and 
vary  their  positions  to  accommodate  themselves  to  the 
magnetic  field  they  chance  to  be  in. 

Magnetize  a  knitting-needle  or  a  piece  of  watch-spring 
by  drawing  its  ends  over  the  ends  of  a  permanent  mag- 
net. If  tested,  it  will  be  found  to  have  poles,  and  to 
behave  like  other  magnets.  Break  it  in  two  in  the 
middle  and  test  each  end ;  each  piece  has  its  poles. 
Break  each  piece  again  and  again  as  long  as  is  prac- 
ticable ;  each  fragment  is  a  complete  magnet,  and  there 
is  every  reason  for  supposing  that  if  this  process  could 
be  carried  on  till  the  iron  molecule  itself  was  reached, 
it  would  be  found  to  be  itself  a  magnet.  This  is  be- 
lieved to  be  the  case.  If  it  be  true,  then  when  such  a 
molecule  is  in  a  position  where  it  is  free  to  turn  about, 
it  will  do  so  if  a  magnetic  field  acts  upon  it  with 
changing  polarity. 

Fill  a  test  tube  three-fourths  full  of  iron  filings.  If 
it  be  held  near  the  poles  of  a  suspended  magnetic  needle, 
every  part  of  it  will  be  attracted  by  the  needle  ;  and  as  the 
needle  is  free  to  turn,  either  pole  will  point  to  any  part 
of  the  tube.  Now  hold  the  tube  against  the  two  poles 
of  a  strong  magnet  and  gently  jar  it  so  as  to  allow  the 
filings  to  arrange  themselves  more  easily.  Remove  it 
from  the  magnet  without  shaking  it,  and  test  for  mag- 


ELECTRICITY    AND    MAGNETISM.  143 

netism  as  before,  and  the  tube  will  be  found  to  have 
poles,  and  will  behave  like  any  other  magnet,  only  it 
will  be  weaker.  Shake  up  the  filings  and  again  test  it, 
and  all  its  polarity  will  be  gone.  The  arrangement  of 
the  parts  has  been  broken  up.  While  it  was  a  magnet 
all  the  like  poles  of  the  individual  particles  faced  the 
same  way.  When  it  was  shaken  up  they  were  all  dis- 
arranged so  their  individual  fields  neutralized  each 
other  ;  there  was  no  longer  any  field  common  to  all. 
If  a  magnetic  phantom,  such  as  was  described,  be  care- 
fully made  and  fixed  upon  a  piece  of  paper  and  sus- 
pended horizontally  by  a  thread  so  as  to  be  free  to 
turn,  it  will  face  north  and  south  like  any  other  magnet, 
and  remain  a  magnet  for  an  indefinite  time. 

All  this  means  that  the  difference  between  a  piece  of 
ordinary  iron  and  a  magnet  is  that  the  molecules  of  the 
latter  all  face  one  way,  while  in  the  iron  they  face  every 
way.  A  current  of  electricity  in  a  coil  makes  the  mole- 
cules of  iron  all  face  one  way,  and  so  does  another 
magnet.  If  they  can  be  fixed  in  such  positions,  the 
piece  remains  a  magnet;  if  they  are  not  so  fixed,  the 
magnetism  is  apparently  lost.  A  piece  of  soft  iron  has 
its  molecular  cohesion  of  position  so  strong  that  the 
molecules  return  to  their  original  positions  as  soon  as 
they  are  free  to  do  so,  that  is,  as  soon  as  the  induction 
pressure  ceases.  A  piece  of  steel  has  carbon  dissem- 
inated through  it  which,  when  it  is  hardened,  prevents 
the  molecules  from  so  easily  changing  back  to  their 
original  positions,  so  it  remains  a  magnet. 

From  this  one  is  to  learn  that  we  do  not  make  iron 
molecules  magnetic  ;  they  are  already  magnetic.  We 


144 


NATURAL    PHILOSOPHY. 


now 


arrange  them  so  their  mag- 
netic fields  shall  not 
neutralize  each  other.  The 
accompanying  diagrams  will 
help  one  to  understand  mag- 
netic arrangement. 

In  I  let  a  represent  a 
single  iron  molecule  —  a 
magnet,  with  a  north  and 
a  south  pole,  N  and  S,  and 
a  field  represented  by  the 
lines  coming  out  on  the  N 
side  and  reentering  on  the 
S  side. 

If  II  he  two  similar  ones 
turned  so  that  the  S  poles 
are  adjacent,  all  the  lines  of 
each  one  will  go  from  S  to 
N,  as  indicated  by  the  ar- 
rows, the  same  as  in  I,  and 
these  opposite  movements 
between  them  producing  op- 
posite stresses,  tend  to  make 
them  separate  from  each 
other.  This  is  called  re- 
pulsion. 

In  III  the  difference  is 
only  that  2  is  turned  round 
so  its  N  side  faces  the  S  side 
of  1.  The  lines  of  1  will 
go  around  2  and  enter  in  its  S  side  and  go  straight 


ELECTRICITY    AND    MAGNETISM.  145 

through  both.  The  field  of  each  is  enlarged,  and  the 
ether  stress  now  acts  so  as  to  crowd  the  two  together. 
This  action  is  called  attraction.  So  if  a  thousand  or 
a  million  are  similarly  arranged  their  fields  are  corre- 
spondingly increased,  and  the  pressure  of  the  fields  acts 
in  one  direction  or  the  other  to  produce  attraction  or 
repulsion. 

Earth's  Magnetism.  —  There  are  many  interesting 
experiments  which  may  be  tried  with  magnets,  but  they 
are  changes  rung  upon  the  preceding  ones.  There  is 
one.  however,  well  worth  repeating  that  emphasizes  some 
of  these  principles.  The  magnetic  or  compass  needle 
points  in  the  direction  it  does  because  the  earth  as  a 
whole  is  a  magnet,  and  has  a  field  which  acts  induc- 
tively upon  all  other  magnets  in  it.  Take  a  rod  of 
iron  two  or  three  feet  long — a  piece  of  gas  pipe,  for 
instance  —  and  bring  it  near  the  poles  of  a  free-turning 
needle.  Hold  the  rod  horizontal,  and  at  right  angles 
to  the  poles  of  the  needle  ;  either  pole  will  be  found  to 
attract  it,  showing  it  has  no  polarity  of  its  own.  Now 
bring  the  rod  over  the  north  pole  of  the  needle  so  as  to 
be  nearly  vertical,  but  two  or  three  inches  from  the 
needle.  The  bar  will  now  repel  the  needle  ;  and  if  the 
bar  l>e  struck  with  a  hammer  while  in  this  position,  the 
needle  will  move  promptly  round,  showing  the  decided 
polarity  of  the  bar,  which  will  strongly  attract  the  south 
end  of  the  needle.  Reverse  the  bar,  and  the  polarity  of 
it  will  lie  reversed  ;  and  if  the  bar  again  be  moved  to  a 
horizontal  position,  it  loses  all  polarity,  and  will  be 
equally  attracted  by  both  poles  of  the  needle.  Thus 


146  NATURAL   PHILOSOPHY. 

the  earth  makes  a  magnet  of  a  piece  of  iron  held  prop- 
erly in  its  magnetic  field,  and  the  polarity  of  the  lower 
end  of  it. is  north. 

The  magnetism  of  the  earth  is  believed  to  be  due  to 
the  large  amount  of  iron  in  it ;  indeed,  there  is  reason 
for  thinking  that  the  most  of  the  interior  of  the  earth 
is  made  up  of  that  element.  We  live  in  a  magnetic 
field,  in  which  the  lines  representing  it  go  from  one 
pole  to  the  other,  high  through  the  air  and  beyond  the 
air. 

Magnetize  a  disk  of  sheet  steel  as  large  as  a  half 
dollar  so  that  its  poles  will  be  on  its  edge  and  opposite 
each  other,  then  make  a  filings  phantom  as  before,  and 
the  lines  will  show  how  they  are  distributed  above  the 
earth's  surface.  The  pillars  of  light  seen  in  auroral 
displays  keep  parallel  with  these  magnetic  lines  of  the 
earth's  field. 

Effects  of  Heat  on  a  Magnet.  —  If  a  nail  lie  heated 
red  hot,  a  magnet  will  not  attract  it  any  more  than  it 
will  a  piece  of  brass  ;  but  when  its  temperature  falls  to 
about  1300°,  it  suddenly  acquires  nearly  its  full  mag- 
netic value,  and  will  at  once  move  promptly  to  the 
magnet  if  it  be  free  to  do  so.  This  phenomenon  means 
that  the  vigorous  heat  vibrations  prevent  the  molecules 
from  assuming  any  regularity  of  position  until  cohesion 
has  become  stronger. 

The  Lifting-  Power  of  a  Magnet  depends  upon  the 
strength  of  its  field,  and  also  upon  how  much  of  the 
field  can  be  made  to  go  through  the  iron  which  it  lifts. 


ELECTUIC1TY    AND    MAGNETISM.  147 

The  strength  of  the  field  depends  upon  how  large  a 
proportion  of  the  molecules  are  properly  faced,  and  also 
upon  how  close  the  poles  are  to  each  other ;  that  is,  a 
U-magnet  will  hold  up  much  more,  proportional  to  its 
weight,  than  a  straight  bar  will ;  and  small  magnets 
are  generally  stronger  proportionally  than  larger  ones. 
A  good  U-magnet  should  hold  up  three  or  four  times 
its  own  weight,  but  small  ones  have  been  made  that 
would  hold  up  twenty-five  times  their  own  weight. 
These  are  values  for  permanent  steel  magnets.  Elec- 
tro-magaets  can  be  made  with  sustaining  power  of  a 
thousand  pounds  per  square  inch.  It  must  be  remem- 
bered that  it  is  ether  pressure  that  causes  all  the  phenom- 
ena in  a  magnetic  field,  and  hence  the  ether  pressure 
may  be  as  much  as  1000  pounds  per  square  inch. 

Electro-Magnetism.  —  In  order  to  detect  the  pres- 
ence of  an  electric  current  in  a  wire  and  also  its  direc- 
tion, the  wire  with  the  current  is  held  over  a  magnetic 
needle,  and  the  needle  turns  this  way  or  that.  One 
may  now  attend  to  a  phenomenon  not  alluded  to  at 
first,  namely,  the  needle  moves  without  touching  the 
wire.  In  a  vacuum  it  moves  still  more  readily,  and 
one  must  conclude  that  there  is  some  kind  of  a  medium 
between  the  wire  and  the  needle  by  which  the  needle  is 
acted  on,  making  it  move.  If  the  current  be  a  strong 
one  —  several  amperes  —  the  needle  will  set  itself  nearly 
at  right  angles  to  the  wire. 

If  a  wire  carrying  a  current  be  thrust  through  a 
piece  of  smooth,  thick  paper,  or,  better  still,  through  a 
hole  in  a  pane  of  glass,  and  filings  of  iron  be  scattered 


148  NATURAL    PHILOSOPHY. 

about  the  wire,  and  if  the  surface  be  gently  tapped  so 
as  to  permit  the  particles  to  arrange  themselves,  if  there 
be  any  pressure  upon  them  tending  to  move  them,  they 
will  be  seen  to  arrange  in  concentric  circles  about  the 
wire  (Fig.  47),  showing  there  is  a  field  about  the  wire 
very  much  as  there  is  a  field  about  a  magnet.  Let  a  wire 
with  a  current  of  several 
amperes  be  dipped  into  iron 
filings  and  they  will  adhere 
to  it,  forming  a  kind  of  coat- 
ing to  it  a  quarter  of  an  inch 
thick  ;  but  on  stopping  the 
current,  they  will  all  fall  off. 
Each  bit  of  iron  was  made  a 
magnet  for  the  time,  with 
north  poles  all  facing  one 
way,  and  so  each  one  attracts 

jj'iu.  rt.  i'ii 

and  sticks  to  the  next  one  in 

front  of  it,  forming  a  circle  about  the  wire.  The 
wire  does  not  attract  them,  but  they  attract  each 
other,  because  they  are  magnets  properly  facing  each 
other. 

Now  let  the  wire  with  the  current  be  bent  so  as 
to  make  a  single  round  loop  three  or  four  inches  in 
diameter,  and  bring  this  loop  near  the  needle,  turning 
the  loop  so  that  first  one  side  and  then  the  other  is 
near  each  pole.  Each  pole  of  the  needle  will  be 
repelled  by  one  side  of  the  loop  and  attracted  by  the 
other,  and  the  needle  will  set  itself,  if  it  be  allowed,  in 
the  middle  of  the  loop  and  at  right  angles  to  it  ;  that 
is,  it  will  be  at  right  angles  to  every  part  of  the  loop. 


ELECTRICITY    AND    MAGNETISM.  149 

By  coiling  the  wire  in  this  way,  a  greater  length  of  it 
with  its  current  can  act  upon  the  needle.  If  two  turns 
be  made,  there  will  be  twice  as  much. wire  and  twice 
the  current  action  upon  the  needle  ;  and  ten  turns  will 
give  ten  times  as  much,  and  so  on.  If,  then,  a  coil  of 
wire  be  made  of  any  shape,  and  a  current  of  electricity 
be  sent  through  it,  one  end  or  side  of  the  coil  will 
attract  and  the  other  will  repel  one  end  of  the  needle. 
That  is  to  say,  a  coil  of  wire  with  one  or  more  turns', 
having  an  electric  current  in  it,  is  a  magnet,  with  all  the 
properties  that  belong  to  a  permanent  magnet,  so  long 
as  the  current  lasts.  It  is  the  current  alone  that  pro- 
duces these  effects,  for  it  is  the  same  whether  the  con- 
ductor be  of  copper,  German  silver,  iron,  or  any  other 
metal.  Such  a  wire  has  a  field  extending  to  an  indefi- 
nite distance  from  it  in  every  direction  at  right  angles 
to  it,  and  the  strength  of  this  field  varies  inversely  as 
the  square  of  the  distance  from  the  wire.  When  the 
wire  is  made  into  a  circle,  the  field  is  condensed  inside 
it,  and  two,  three,  and  more  turns  make  it  two,  three, 
or  more  times  stronger. 

Iron  is  a  much  better  conductor  of  magnetic  stress 
than  is  the  air.  If  a  piece  of  iron  be  placed  in  the  coils, 
the  magnetic  field  of  the  wire  is  absorbed  by  it,  and  it 
becomes  a  magnet  by  induction.  Its  strength  depends 
upon  the  strength  of  the  current,  that  is,  upon  how 
many  amperes  the  wire  carries;  also  upon  how  close 
the  wire  is  to  the  iron,  and  is  greatest  when  the  wire 
is  wound  upon  the  iron  ;  the  strength  of  the  magnet 
depends  also  upon  how  much  wire  is  wound  about  it, 
that  is,  how  many  turns  there  are.  The  product  of  the 


150  NATURAL   PHILOSOPHY. 

current  in  amperes,  multiplied  by  the  number  of  turns 
of  wire,  is  called  ampere  turns. 

Such  a  magnet  is  called  an  electro-magnet,  and  as 
already  stated,  it  can  be  made  very  much  stronger  than 
a  permanent  magnet.  Its  poles,  too,  can  be  reversed 
by  reversing  the  direction  of  the  current,  which  process 
reverses  the  position  of  the  iron  molecules.  The  rota- 
tion of  the  molecules  brought  about  in  this  way  re- 
sults in  friction  among  them  in  the  iron,  which  becomes 
heated,  and  energy  is  thus  wasted.  This  phenomenon 
is  called  hysteresis. 

Electro-Magnetic  Induction.  —  An  electro-magnet 
is  made  by  creating  a  magnetic  field  about  a  piece  of 
iron.  The  magnetic  field  may  come  from  another 
magnet  already  made,  or  from  a  current  of  electricity 
in  a  coil  of  wire  about  the  iron.  The  action  is  a  revers- 
ible one  ;  that  is,  a  magnetic  field  produced  in  a  coil  of 
wire  will  induce  a  current  of  electricity.  This  is  what 

was  shown  on 
page  117,  where 
was  described 
the  second  meth- 
od of  generat- 
ing electricity  by 

moving  a  coil  of  wire  in  a  magnetic  field.  If,  instead 
of  employing  a  permanent  magnet  as  in  that  experiment, 
we  should  take  an  electro-magnet  and  wind  it  with  a 
separate  coil,  so  that  the  first  coil  could  be  connected  with 
a  battery  or  other  source  of  electricity,  while  the  second 
coil  could  be  connected  with  a  galvanometer,  as  in 


•     ELECTRICITY    AND    MAGNETISM.  151 

figure  48,  where  the  inner  coil  represents  the  wire  for  an 
ordinary  electro-magnet  connected  so  that  by  pressing 
the  key  the  current  could  be  sent  through  it,  the  outer 
coil  about  the  same  rod  leads  to  the  galvanometer  G. 
Every  time  the  key  closes  the  battery  circuit  the  iron 
is  made  a  magnet,  a  field  is  produced  about  it,  and  the 
second  coil  has  a  current  induced  in  it  which  will  show 
itself  by  the  movement  of  the  galvanometer  needle. 
Holding  the  key  down,  the  needle  will  come  to  rest  at 
0,  showing  there  is  no  current  present  in  the  second 
wire.  On  opening  the  first  circuit,  the  magnet  will 
lose  its  magnetism,  the  field  will  be  destroyed,  and  the 
needle  will  again  show  a  current  in  the  second  circuit, 
but  in  the  opposite  direction  from  the  former  one.  This 
will  happen  as  often  as  the  first  circuit  is  closed  and 
opened. 

If  a  key  be  so  made  as  to  reverse  the  direction  of 
the  current  instead  of  breaking  it  in  the  first  circuit, 
which  is  called  the  primary  circuit,  the  current  in  the 
other,  which  is  called  the  secondary  circuit,  will  be 
much  stronger.  Such  a  magnet  provided  with  two 
separate  coils  or  circuits  is  called  an  induction  coil.  Of 
course  it  may  be  made  of  any  shape  or  size,  and  have 
many  uses,  some  of  which  will  be  mentioned  further  on 
in  this  book.  Here  it  will  be  sufficient  to  point  out  the 
relation  of  the  two  coils  to  each  other. 

Suppose  we  have  a  bar  of  iron  with  two  similar  coils 
upon  it ;  that  is,  both  have  the  same  number  of  turns 
of  wire  of  the  same  size.  This  can  be  arranged  by 
winding  the  wire  on  two  spools,  and  putting  one  on 
each  end  of  the  magnet.  Either  of  these  may  be  used 


152  NATURAL   PHILOSOPHY. 

as  a  primary  circuit.  Suppose  there  be  100  turns  of 
wire  on  each  spool,  and  a  battery  be  connected  to  the 
primary  coil  that  shall  give  10  volts'  pressure  in  it,  and 
a  key  for  reversing  the  current  be  joined  in  the  circuit ; 
then  every  time  the  current  in  the  primary  circuit  is 
reversed,  there  will  be  a  pressure  of  10  volts  in  the  sec- 
ondary coil.  If  there  were  1000  turns  in  the  secondary 
instead  of  100,  the  pressure  in  it  would  be  100  volts  ; 
that  is,  the  pressure  in  the  secondary  of  an  induction 
coil  varies  as  the  number  of  turns  of  wire  in  the  coil ; 
the  size  of  the  wire  makes  no  difference  in  this  particu- 
lar. The  pressure  in  the  secondary  circuit  will  be  to 
the  pressure  in  the  primary  circuit,  as  the  number  of 
turns  of  wire  in  it  is  to  the  number  of  turns  in  the 
primary;  that  is, 

V  in  primary  :  V  in  secondary  :  :  t  in  primary  :  V  in  secondary, 

where  F'and  V  are  volts  and  t  and  t'  are  the  number 
of  turns  of  wire.  This  will  be  true  only  when  the 
primary  current  is  alternating  in  direction. 

On  page  149  it  is  pointed  out  that  the  strength  of  an 
electro-magnet  depends  upon  the  ampere  turns  of  wire, 
and  the  same  is  true  of  the  secondary  wire. 

Thus,  if  there  be  100  turns  and  1  ampere  in  the  pri- 
mary and  1000  turns  in  the  secondary,  the  current  in 
the  latter  will  be  such  that  the  ampere  turns  in  it 
equal  the  ampere  turns  in  the  primary.  Since  in  the 
primary  there  are  100  X  1  =  100  ampere  turns,  there 
must  be  100  ampere  turns  in  the  secondary  ;  there  are 
1000  turns  of  wire  in  the  secondary,  the  current  in  it 
will  be  Yj0^  =  one-tenth  of  an  ampere.  If  the  primary 


ELECTRICITY   AND   MAGNETISM.  153 

has  1000  turns  and  1  ampere,  the  secondary  with  100 
turns  will  have  10  amperes. 

As  t  in  primary  :  V  in  secondary  :  :  c'  in  secondary  :  c  in  primary. 

This  is  the  principle  involved  in  induction  coils,  and 
when  employed  thus  it  is  evident  that  the  voltage  in 
the  secondary  is  raised  or  lowered  from  that  in  the 
primary  by  simply  varying  the  proportional  number  of 
turns  of  wire  in  it.  As  an  induction  coil  transforms 
high  voltage  to  low,  or  vice  versa,  it  is  called  a  trans- 
former. 

The  energy  in  an  electric  circuit  has  been  explained 
as  being  equal  to  the  product  of  the  pressure  in  volts  mul- 
tiplied by  the  current  in  amperes.  This  is  equally  true 
for  electro-magnets  and  transformers.  In  primary, 
ec  =  e'c'  in  secondary.  For  instance,  let  the  voltage 
in  the  primary  of  a  transformer  be  1000,  and  the 
current  1  ampere,  the  energy  ec  =.1000  X  1  =  1000 
watts.  The  transformer  hands  over  this  energy  from 
the  primary  circuit  to  the  secondary  ;  it  does  not  in- 
crease it,  it  may  diminish  it  by  some  losses.  If  the 
voltage  of  the  secondary  is  reduced,  say  to  100  volts, 
still  the  number  of  watts  is  e'c'  =  1000,  and  as  e'  =  100, 
c'  must  equal  10. 

Heating:  Power  of  an  Electric  Current.  —  An  elec- 
tric current  always  heats  the  conductor  through  which 
it  goes  ;  how  much  it  will  be  heated  depends  upon  a 
number  of  factors.  If  746  watts  are  equal  to  a  horse- 
power or  550  foot>-pounds  of  work  per  second,  then 
I^H  =  .75  foot-pounds  is  the  horse-power  equivalent  of 


154  NATURAL   PHILOSOPHY. 

one  watt.  As  one  heat  unit  equals  778  foot-pounds,  1 
foot-pound  is  y^  of  a  heat  unit,  and  .75  of  a  foot- 
pound .75  X  Y}s  =  .00096.  This  means  that  1  watt, 
in  1  second,  will  heat  a  pound  of  water  .00096°,  and 
may  be  considered  as  the  heat  equivalent  of  a  watt  in 
a  second. 

From  Ohm's  Law  we  have  J2=  OR.  If  this  value  of 
E  be  substituted  for  the  E  in  EC,  which  represents 
electrical  energy,  we  shall  have  OR  X  C=  C*R  as  an 
equivalent  expression  for  electrical  energy  in  terms  of 
current  and  resistance.  It  shows  that  the  eneryy  or 
heating  power  is  proportional  to  the  square  of  the  current, 
and  this  must  be  remembered.  Two  amperes  will  heat 
4  times  as  much  as  1,  and  10  amperes  100  times  as 
much,  and  so  on.  If  the  resistance  be  doubled,  the 
heat  will  be  doubled,  that  is,  the  heating  is  proportional 
to  the  resistance.  It  might  be  supposed  that  if  the 
current  was  maintained  for  2  seconds,  it  would  develop 
twice  as  much  as  it  would  in  1  second,  and  in  t  seconds 
t  times  as  much.  Putting  all  these  factors  together, 
the  amount  of  heat  developed  is  equal  to  .00096  X  ^t. 

For  instance,  how  much  heat  would  be  developed  in 
1  minute  by  a  current  of  10  amperes  in  a  wire  having 
3  ohms  resistance  ? 

.00096  X  102  X  3  X  60  =  17.28,  or  1  pound  of  water 
would  be  heated  17.28°  by  it. 

An  apparatus  suitable  for  studying  the  heating 
power  is  shown  in  the  adjacent  figure  (49).  It  is  a 
bottle  for  holding  a  known  quantity  of  water,  through 
the  cork  of  which  is  fixed  a  coil  of  wire  of  known 
resistance,  submerged  in  the  water ;  a  thermometer 


ELECTRICITY    AND    MAGNETISM. 


155 


extends  into  the  water,  on  which  the  rise  in  tempera- 
ture may  be  observed  during  the  passing  of  the  current. 
The  temperature  to  which  a  given  body  will  be 
raised  by  a  definite  amount  of  heat  depends  upon 
its  specific  heat  (p.  92).  As  water  has 
the  highest  specific  heat,  its  temperature 
is  changed  the  least  by  a  given  amount 
of  heat.  The  specific  heat  of  iron  is 
.1138.  The  current  of  electricity  that 
would  heat  a  pound  of  water  17.28°  in 
1  minute  would  heat  a  pound  of  iron 

17  28 

'^    =152°.     In  any  case,  the  heat 
.lloo 

required  may  be  readily  computed  if 
the  resistance,  current,  time,  and  specific 
heat  be  known,  the  formula  being 
.00096  X  c^rt 

spec,  heat 

If  the  resistance  be   large   and  the 
current  weak,  the  change  in  tempera- 
ture may  not  be  very  noticeable.     Telegraph  lines  are 
not  much  heated  by  the  currents  employed,  but  when 
the  current  is  a  hundred  or  a  thousand  amperes,  the 
heating  effect  is  ten  thousand  or  a  million  times  greater 
than  when  it  is  of  one  ampere,  and  metals  and  most 
refractory  things  may  be  fused. 

In  the  electric-welding  process  the  ends  to  be  welded 
are  pressed  tightly  together,  while  a  current  is  sent 
through  their  junction  strong  enough  to  raise  the  parts 
to  a  welding  heat.  .  When  they  become  cold,  the  junc- 
tion is  solid.  The  resistance  is  much  greater  at  the 


156 


NATURAL   PHILOSOPHY. 


place  of  contact  than  elsewhere,  and  therefore  the  heat 
is  chiefly  developed  there. 

The  same  principle  of  heating  is  applicable  to  cook- 
ing apparatus.  A  coil  of  German  silver  wire  may  be  kept 
at  any  desirable  temperature  by  a  proper  current  of  elec- 
tricity. Ordinarily  8  or  10  amperes  through  a  coil  of 
6  or  8  ohms'  resistance  is  sufficient.  This  is  not  far 
from  an  electrical  horse-power.  cV—  102  X  8  =  800 
watts. 

Another  interesting  method  of  electrical  heating  of 
metals  has  been  discovered.  If  a  current  of  40  or  50 

amperes  be  sent 
through  a  bucket 
of  water  made 
alkaline  and  a 
better  conductor 
by  adding  some 
sodium  carbon- 
ate to  it,  a  high 
degree  of  heat 
is  developed  at 
the  terminals 
dipping  into  the  liquid.  If  one  of  these  terminals  be  a 
large  sheet  of  lead  or  of  carbon,  while  the  other  be 
a  rod  of  iron  to  be  heated  (Fig.  50),  the  latter  may 
l>e  fused  under  the  water  in  a  few  seconds.  The 
principle  here  is  the  same  as  the  preceding,  the  con- 
ditions being  a  strong  current  and  resistance. 


Fio.  50. 


ELECTRICITY    AND    MAGNETISM. 


157 


ELECTRIC    LIGHTING. 

The  Arc  Tag-lit.  —  When  an  electric  circuit  is  broken, 
a  spark  may  be  seen  at  the  place.  If  the  pressure  be 
40  or  50  volts,  the  current  is  not 
broken  when  the  metallic  circuit  is 
broken,  and  the  ends  of  the  circuit 
may  be  separated  a  distance  that  de- 
pends upon  the  voltage  and  the  kind 
of  material  of  the  broken  conductor. 
It  is  customary  to  use  sticks  of  carbon, 
so  fixed  that  the  current  keeps  them 
separated  about  the  eighth  of  an  inch 
(Fig.  51),  and  raises  their  ends  to  a 
white  heat;  they  then  give  a  blight 
light.  The  energy  is  spent  in  the 
carbon  tips.  If  the  voltage  be  45  and 
the  current  be  10,  EC  =±5  X  10  = 
450  watts;  |;>o  __  g  of  a  horse-power. 
This  electric  energy  is  measured  by 
connecting  an  ammeter  in  circuit  with 
the  arc  lamp,  and  connecting  the  ter- 
minals of  a  voltmeter  to  the  two 
carbons. 

In  Fig.  52,  L  is  the  lamp,  A  the 
ammeter,  and  V  the  voltmeter,  CC  the 
arc-light  circuit. 

All  lamps  in  the  circuit  require  the 
same   number  of  volte.     The    voltage  in  an    arc-light 
circuit   depends    upon    the    number  of   lamps  lighted. 
The  lamps  are  all  in  series,  and  the  current  is  the  same 


158 


NATURAL    PHILOSOPHY, 


for  all,  and  is  generally  9  or  10  amperes.     There  are 

seldom  more  than  100  such  lamps  in  one  circuit,  and  as 

each  one  requires 
45  volts,  the  dy- 
namo must  provide 
45  X  100  =  4500 
volts  and  10  am- 
FIG-52-  peres.  The  EC  of 

the  circuit  is  4500 X  10  =  45000  watts,  450|o  =  60  — 

horse-power. 

An  arc  lamp  using  450  watts  gives  a  light  equal  to 

about  800  candles.      Search  lights  use  a  current  of  100 

and  sometimes  200  amperes  at  45  volts, 

and  the  beam  reflected  from  a  concave 

mirror  behind  the  lamp  is  concentrated 

into  a  dense  beam,  reckoned  at  millions 

of  candles. 

The  Incandescent  Light.  —  This  is 
the  name  given  to  the  light  from  a 
thread  or  filament  of  carbon,  which  is 
heated  white-hot  by  a  current  of  elec- 
tricity passing  through  it.  When  car- 
bon is  thus  heated  in  the  air,  it  not 
only  gives  out  light,  but  it  is  consumed ; 
that  is,  its  surface  molecules  combine 
with  oxygen  of  the  air,  forming  gas.  To 
prevent  this  action  the  filament  is  en- 
closed in  a  glass  bulb  from  which  the  air 
has  been  exhausted.  The  lamp  is  familiar  enough  to  all 
(Fig.  53).  The  light  from  it  is  directly  due  to  the  high 


.     ELECTRICITY    AND    MAGNETISM.  159 

temperature  which  the  electric  current  produces,  not  to 
electricity  itself ;  so  the  stronger  the  current,  the  higher 
the  temperature.  Most  such  lamps  have  filaments  of 
such  a  size  that,  with  a  current  of  .5  or  .6  of  an  ampere, 
a  linear  inch  gives  the  light  of  2  or  3  candles.  The 
longer  the  filament,  the  more  light.  A  sixteen-candle- 
power  lamp  has  a  filament  about  8  inches  long.  Such 
lamps  are  adapted  to  particular  electric  pressure,  as  50 
volts  or  110  volts. 

A  110- volt  lamp  using  a  current  of  .6  of  an  ampere 
uses  110  X  .6  =  66  watts  of  electrical  energy.  If  the 
lamp  now  gives  the  light  of  16  candles,  each  candle 
requires  ||  =  4.1  watts.  By  increasing  the  current  to 
.7  of  an  ampere,  the  light  may  be  increased  to  25  candles, 
and  the  amount  of  energy  per  candle  is  lessened,  for 

no  4 

112  X  .7  =  78.4  watts,  and  ifl!  =  3.1  watte.      By  in- 

aO 

creasing  the  voltage  to  115,  the  current  may  rise  to  as 
much  as  an  ampere,  and  the  light  to  100  candles  ;  but 
when  this  is  done,  the  filament  is  soon  destroyed. 

If  one  will  recall  what  is  happening  when  a  body  is 
heated,  —  that  its  molecules  are  violently  beating  against 
each  other,  and  at  the  surface  are  being  evaporated  witli 
a  rapidity  which  depends  upon  the  temperature,  —  he 
will  understand  what  happens  to  an  incandescent  lamp 
filament  when  the  glass  becomes  blackened  and  the  fila- 
ment broken  by  the  vigor  of  the  molecular  vibrations. 

Unlike  arc  lamps,  which  are  arranged  in  series,  incan- 
descent lamps  are  arranged  like  the  steps  on  a  ladder  ; 
this  is  called  multiple  connection  :  thus  (Fig.  54),  a  and  b 
are  wires  from  the  dynamo,  and  have  an  electric  pres- 


160  NATURAL   PHILOSOPHY. 

sure  between  them  of  50  or  110  volts.  Any  lamp 
having  its  terminals  connected  to  these  2  wires  will 
have  a  current  through  it,  the  strength  of  which  de- 
pends upon  the  resistance  of  the  lamp.  Thus,  if  the 
voltage  be  50,  and  the  lamp  has  a  resistance  of  100 
a  ohms,  the  current 

ft     ft     ft     ft     ft     ft     ft        will  be  ^  =  .5 
b-  -  of    an    ampere. 

FIG   54 

The  watts  would 

be  50  X  -5  —  25,  and,  at  4  watts  per  candle,  such 
a  lamp  would  give  about  6  candle-power. 

One  may  now  see  the  relation  between  horse-power 
and  electric  lights.  The  electric  horse-power  is  equal 
to  746  watts.  If  an  incandescent  lamp  requires  4 
watts  per  candle,  a  horse-power  will  give  -7--|£=186 
candle-power,  which  may  be  distributed  among  as  many 
or  as  few  lamps  as  one  pleases.  If  each  lamp  gives  16, 
there  maybe  JT^=11  lamps  per  horse-power;  if  the 
lamps  give  but  10,  there  may  be  18  -J-  such  lamps  to  the 
horse-power. 

If  an  arc  light  consumes  450  watts  =  .6  horse-power, 
and  gives  light  of  800  candle-power,  a  whole  horse- 
power would  give  1333  candles,  seven  times  as  much  as 
with  the  incandescent  system.  And  if  746  watts  give 
1333  candles,  each  candle  requires  f^fa  of  a  watt,  or 
only  little  more  than  half  a  watt  per  candle. 

The  expenditure  of  energy  in  an  incandescent  lamp  may 
be  measured  in  precisely  the  same  way  as  in  an  arc  lamp. 

The  Dynamo.  —  If  a  wire  be  put  between  the  poles 
of  a  U-shaped  magnet,  it  will  be  in  the  strongest  part 


ELECTRICITY    AND    MAGNETISM. 


161 


of  the  magnetic  field.  If  it  be  moved  towards  the 
bend  in  the  magnet,  an  electric  pressure  will  be  devel- 
oped in  it,  the  direction  of  which  is  indicated  by  the 
arrowhead  upon  the  wire  (Fig.  55);  and  if  the  ends  be 
connected  to  a  galvanometer  of  proper  delicacy,  its 
needle  will  move.  When  the  wire  is  moved  back  a 
current  is  induced  in  the  opposite  direction. 

If  two  wires  be  thus  moved  at  the  same  time,  each 
will  have  a  current  induced  in  it  in  the  same  direction, 


and  so  on  for  as  many  wires  as  may  be  thus  moved.  If 
the  two  are  parts  of  the  same  wire,  as  indicated  in 
Fig.  56,  the  two  pressures  will  balance  each  other, 
and  no  current  at  all  will  flow.  If,  however,  the  loop 
of  wire  be  fixed  to  rotate  so  that  its  mechanical 
motions  will  be  opposite,  —  one  going  up  through  the 
field  while  the  other  is  going  down,  as  in  Fig.  57,  —  a 
current  will  flow  around  the  wire  as  the  arrows  point. 
For  one-half  of  the  revolution  the  current  will  be  in 
one  direction,  and  the  other  half  it  will  IK?  in  the  oppo- 
site ;  it  is  therefore  called  an  alternating  current.  If  the 


162 


NATURAL   PHILOSOPHY. 


two  ends  of  the  wires  be  connected  to  the  two  halves 
of  a  metal  cylinder  which  are  insulated  from  each  other 
upon  the  axis,  and  against  which  some  springs  make 
contact  (Fig.  58),  the  current  may  be  led  off  by  wires 
to  any  place  where  it  is  wanted,  and  it  will  be  con- 
tinuously in  the  same  direction. 

This  device  for  directing  the  current  is  called  a  com- 


FlG.  57.  FIG.  58. 

mutator  —  an  exceedingly  important  part  of  electrical 
machines.  Such  a  current  is  called  a  constant  or  direct 
current. 

By  adding  more  turns  of  wire  to  rotate  together  in 
the  same  field,  the  pressure  is  increased  proportionally, 
it  depends  also  upon  the  rate'  of  rotation.  The  pressure 
is  also  dependent  upon  the  strength  of  the  magnetic 
field ;  the  stronger  the  field,  the  higher  the  voltage. 
The  strength  of  the  field  may  be  greatly  increased  by 
putting  iron  between  the  poles  of  the  magnet,  as  it  is  a 
better  conductor  of  magnetism  ;  hence  the  wire  is  wound 
upon  iron,  generally  in  cylinder  or  ring  form,  and  the 
poles  of  the  magnet  are  curved  so  as  to  be  as  close  as 
possible  to  the  rotating  parts.  The  large  magnet  N  S 


ELECTRICITY    AND    MAGNETISM. 


163 


(Fig.  59),  that  provides  the  magnetic  field,  is  called  the 
field  magnet,  and  the  rotating  part  of  iron  with  its 
coils  of  wire  is  called  the  armature.  Together  they 
constitute  a  dynamo. 

The  first  machines  of  this  kind  were  made  with  field 
magnets  of  steel  permanently  magnetized.  Now  they 
are  made  of  soft  iron  with  coils  of  wire  about  them, 


Lamps  in  Series 


that  is,  they  are  electro-magnets,  and  the  current  gen- 
erated in  the  armature  is  made  to  pass  through  the  field- 
magnet  coils  (Fig.  59);  hence  the  stronger  the  current, 
the  stronger  the  magnet.  Such  an  arrangement  is  called 
a  series  dynamo,  and  is  the  one  generally  employed  for 
arc  lighting. 

In  some  dynamos  only  a  portion  of  the  current  gen- 
erated goes  through  the  field-magnet  coils  ;  the  remainder 
goes  through  the  main  circuit,  to  be  used  for  commercial 


164 


NATURAL    PHILOSOPHY. 


purposes.  Such  a  machine  is  called  a  shunt  dynamo 
(Fig.  60),  and  is  the  kind  employed  in  incandescent 
lighting.  When  run  at  uniform  speed,  it  is  capable 


Lamps  in  Parallel.         y  y  ^ 


of  giving  a  uniform  electric  pressure,  as  50  volts  or  110 
volts  throughout  its  main  circuit;  the  lamps  are  con- 
nected in  parallel  circuits  to  the  larger  wires,  called 
mains. 

Either  of  these  machines  may  be  made  of  any  size, 
and  their  field  magnets  may  be  shaped  in  any  conven- 
ient way  without  changing  their  electrical  qualities. 

A  dynamo  is  a  machine  for  transforming  mechanical 
energy  into  electrical  energy.  Its  efficiency  may  be  as 
high  as  97^>.  That  is,  if  a  steam-engine  of  100  horse- 
power be  made  to  drive  a  dynamo,  and  if  there  be  no 
loss,  the  electrical  energy,  EQ,  would  be  746  X  100  = 


ELECTRICITY    AND    MAGNETISM. 


165 


74,600  watts.  That  would  be  100^  efficiency.  As  a 
matter  of  fact  it  would  be  no  more  than  74,600  X  .97  = 
72,362  watts,  and  might  be  less  on  account  of  heating, 
friction,  and  so  on.  As  it  is,  however,  it  is  one  of  the 
most  perfect  machines  man  has  yet  made.  The  dynamo 
may  be  made  of  any  size  and  of  any  horse-power,  up  to 
5000  or  more,  so  as  to  furnish  electrical  energy  of  any 
pressure  and  current. 

The  Electric  Motor.  —  This  in  structure  is  simply 
a  dynamo.  When  a  current  of  electricity  from  some 
other  source  is  made  to  traverse  its  armature  coils,  the 
magnetic  reaction  turns  the  armature,  and  it  may  be 


FIG.  6i. 


made   to  do  work.      When  thus   employed,  the  same 
machine  is  called  a  motor  (Fig.  61). 

Tlie  function  of  a  motor  is  to  transform  electrical  energy 
into  mechanical  energy,  and  its  efficiency  is  also  high. 


166 


NATURAL    PHILOSOPHY. 


It  should  be  remembered  that  electrical  energy  is 
always  derived  by  transformation  from  some  other  kind 
of  energy,  and  can  do  no  more  mechanical  or  other  kind 
of  work  than  an  equal  amount  of  energy  of  any  other 
kind  can  do. 


THE  TELEGRAPH. 

I.  The  Electro-Magnetic.  —  The  ability  a  current 
of  electricity  has  to  make  a  magnet  of  a  piece  of  iron, 
which  can  attract  to  itself  another  piece  of  iron  and 
stop  attracting  it  when  the  current  stops,  is  employed 
for  making  signals  at  a  distance. 
In  Fig.  62  e  is  an  electro- 
magnet, a  the  iron  armature 
upon  an  arm,  s  a  spring  to  keep 
• — •  ^  ^  the  armature  up  from  the  mag- 
" — i — "•  •• — i  net  and  against  the  stop  above. 

A  corresponding  stop  below 
prevents  the  armature  from 
quite  touching  the  end  of  the 
magnet.  In  Fig.  63  B  is  a  bat- 
tery or  other  source  of  electri- 
city ;  k  is  a  key  for  closing  the 

circuit.  As  often  as  the  key  closes  the  circuit  a  current 
goes  through  the  coil,  making  e  a  magnet  which  pulls 
down  the  armature  a.  This  action  is  so  quick  that  the 
stroke  of  the  armature  can  be  plainly  heard,  taking 
place  whenever  the  key  k  is  worked  by  the  hand.  A 
series  of  strokes  made  faster  or  slower  can  be  produced, 
and  these  have  been  constructed  into  a  telegraphic 


ELECTRICITY    AND    M  A<  J  NKTISM 


167 


alphabet,  the  letters  of  wliieh  can  be  recognized  by  the 
ear,  the  length  of  time  the  key  is  held  down  being  told 
by  the  sound  of  the  up-strokes.  Thus  a  short  and  a 


long  hold  give  the  letter  a,  a  long  and  three  short  ones 
the  letter  i,  and  so  on.  This  is  called  reading  by  xoumi, 
and  the  magnet  adapted  for  this  work  is  called  a  son  tt  •/•'/• 
(Fig.  64).  How  long  the  line  is  does  not  much  matter, 
for  it  is  the  current  which  is  needed  for  the  electro- 
magnet, and  the  increased  resistance  of  a  longer  line 
may  be  met  by  using  higher  pressure.  Thus,  suppose 
a  sounder  requires  the  tenth  of  an  ampere  to  work  it 
properly,  and  has 
a  resistance  of  5 
ohms.  If  the  line 
be  a  mile  long  with 
the  resistance  of 
10  ohms,  and  the 
pressure  is  5  volts, 
the  current  will  be 
5 


=.33  of  an 


FIG.  64. 


ampere.  If  the  line  be  made  ten  miles  long,  the  resist- 
ance would  be  105  ohms  ;  and  in  order  to  get  .1  of  an 
ampere,  there  will  need  to  be  105  X  -1  =  10.5  volts. 
For  long  lines  it  is  customary  to  use  magnets  that  will 


168  NATURAL    PHILOSOPHY. 

work  promptly  with  currents  no  stronger  than  .01  of  an 
ampere,  and  often  these  are  so  made  that  in  working 
they  open  and  close  another  electric  circuit  which 
extends  still  farther  away.  The  latter  device  is  called 
a  relay.  The  resistance  thus  overcome  may  be  as  much 
as  150  ohms. 

A  continuous  current  implies  a  continuous  conducting 
circuit  which  must  not  be  broken  ;  and  a  conducting 
circuit  means  a  continuous  line  of  conductor  from  one 
terminal  of  the  battery  or  other  source  of  electricity  to 
the  other  terminal.  It  is  not  necessary  for  this  con- 
ductor to  be  wire ;  the  earth,  when  damp,  acts  as  a 
conductor  if  the  ends  of  the  wires  are  buried  in  it.  A 
buried  plate  of  copper  or  iron  at  the  end  of  each  wire 
seems  to  decrease  the  resistance  of  the  circuit,  yet  each 
such  buried  plate  adds  about  100  ohms  to  the  circuit ; 
200  ohms  would  be  no  more  than  the  resistance  of  15 
or  20  miles  of  wire.  So  if  the  line  be  a  long  one, 
only  one  wire  need  be  stretched  between  stations. 

II.  The  Chemical  Telegraph.  —  If  a  current  of  elec- 
tricity goes  from  an  iron  point  through  a  piece  of  paper 


FIG.  65. 


moistened  with  the  ferrocyanide  of  potassium,  it  makes 
a  blue  mark.  If  the  paper  be  drawn  along,  it  will  make 
a  blue  line. 


ELECTRICITY    AND    MAGNETISM. 


169 


Suppose  R  represents  a  metallic  roller  on  which  the 
strip  of  paper  p  is  drawn,  while  the  iron  finger  e  touches 
upon  it,  the  finger  being  connected  to  the  battery  B. 
When  the  key  K  closes  the  circuit,  a  blue  mark  will 
be  made  where  e  touches  the  paper.  If  K  be  worked, 
say  once  a  second,  while  p  is  being  drawn  along  in  the 
direction  of  the  arrow,  there  will  be  a  series  of  blue 
marks  made.  If  the  key  be  worked  as  for  the  electro- 
magnetic alphabet,  there  will  be  a  series  of  dots  and 
dashes  corresponding  to  the  letters,  which  may  be  read 
by  those  acquainted  with  them.  As  the  action  is 
purely  a  chemical  one,  this  telegraph  is  called  the 
chemical  telegraph.  It  makes  no  sound,  is  much  more 
sensitive  than  the  former  one  described,  and  can  be 
worked  at  a  higher  rate  of  speed. 

Mechanical  Transmitters  are  made  by  punching 
holes  and  slots  corresponding  to  the  letters  in  the  tele- 


170  NATURAL   PHILOSOPHY. 

graphic  alphabet  in  long  strips  of  paper,  and  drawing 
this  over  a  metallic  roller.  A  metallic  finger  presses 
upon  the  paper,  and  falls  into  the  holes  as  the  strip  is 
pulled  along,  and  so  completes  the  electric  circuit  for 
a  longer  or  a  shorter  time.  The  chemical  telegraphic 
receiver  makes  corresponding  blue  marks  on  a  strip  of 
paper  ;  this  is  done  at  the  rate  of  four  or  five  hundred 
words  a  minute.  With  the  ordinary  hand-key,  thirty  or 
forty  words  a  minute  is  a  good  working  rate. 

THE    SPEAKING   TELEPHONE. 

The  Magnetic  Telephone.  —  If  one  holds  a  sheet 
of  paper  in  front  of  his  mouth  and  sings  or  talks,  lie 
can  feel  the  jar  of  the  vibrations  that  the  air  waves  pro- 
duce on  the  paper.  It  moves  to  and  fro  as  many  times 
a  second  as  there  are  air  waves  per  second.  If  he  does 
the  same  with  a  thin  piece  of  sheet  iron,  the  same  effect 


FIG.  67. 

follows,  only  not  quite  so  appreciably,  as  the  iron  has 
more  mass  to  move.  If  the  iron  is  brought  up  near  the 
pole  of  a  magnet  about  which  is  a  coil  of  wire,  the 
inductive  action  between  the  magnet  and  the  iron 
causes  electric  currents  to  go  on  in  the  wire  this  way 
or  that,  as  the  plate  moves  towards  or  away  from  the 
pole.  It  is  a  kind  of  dynamo  in  which  the  armature  is 


ELECTRICITY    AND   MAGNETISM. 


171 


moved  by  sound  waves.  If  connecting  wires  lead  to  a 
distant  similar  instrument,  the  currents  will  cause  the 
attraction  between  the  magnet  pole  and  its  iron  arma- 
ture to  be  now  stronger  and  now  weaker,  and  will 


make  the  plate  vibrate  in  the  same  way  as  the  plate 
in  the  first  instrument  vibrated  ;  and  if  the  first  vibra- 
tions were  produced  by  speech  at  the  arrow  (Fig.  67), 
an  ear  at  the  other  instrument  will  hear  what  is  said, 
the  latter  instrument  acting  as  a  motor. 

If  the  plate  spoken  to  be  made  to  press  more  or  less 
hard  upon  a  knob  of  hard  carbon    through    which    a 


current  from  a  battery  is  going  (Fig.  68),  the  varying 
pressure,  when  sound  waves  act  on  the  plate,  Avill  cause 
the  current  to  vary  in  a  corresponding  way,  and  the  same 
result  is  produced  at  the  listening  instrument  or  receiver, 


172 


NATURAL    PHILOSOPHY. 


as  it  is  commonly  called.     The  instrument  spoken  to  is 
called  the  transmitter. 

Generally  the  transmitter  is  combined  with  a  small 
induction  coil  (Fig.  69),  so  the  battery  current  is  in  a 
very  short  circuit,  the  secondary 
wire  going  to  the  receiver.  This 
arrangement  is  much  more  efficient 
than  the  former  one,  and  by  its 
means  one  may  talk  to  another  a 
thousand  miles  away. 

The  Static  Telephone.  —  There 

are  several  other  methods  by  which  sounds  of  any  kind 
may  be  reproduced  by  electricity.  One  of  them  is  by 
means  of  electrical  attraction  as 
distinguished  from  magnetic  at- 
traction. Thus,  if  a  wire  from 
any  source  of  electricity  be  con- 
nected to  a  metallic  plate  a  (Fig. 
70)  by  some  method,  another 
metallic  plate  b  near  it  will  be 
attracted  by  it  whenever  the 
plate  a  is  electrically  charged. 
If  it  be  prevented  from  making 
contact  with  a  by  separating  the 
two  by  a  non-conducting  ring, 
the  middle  of  the  plate  b  will 
bulge  toward  a,  and  its  own 
elasticity  will  restore  it  to  flat- 
ness  when  the  attraction  stops.  Hence  a  series  of 
electric  charges  from  a  source,  such  as  a  transmitter 


FIG.  71. 


ELECTRICITY    AND    MAGNETISM.  173 

with  induction  coil  for  high  pressure,  will  make  the 
plate  b  move  in  a  corresponding  way,  and  speech  may 


FIG.  72. 

be  heard  by  listening  at  b.     The  whole  arrangement  is 
shown  in  diagrams  (Figs.  71  and  72). 

TELEGRAPHING  "WITHOUT    "WIRES. 

By  Conduction. —  When  the  two  ends  of  an 
electric  circuit  are  buried  in  the  earth,  the  current 
through  the  earth  spreads  out  in  every  direction,  but 
chiefly  goes  toward  the  opposite  terminal.  .Thus,  a  and 
b  (Fig.  73)  represent  the  ground  terminals  of  a  circuit, 
the  stations  being  connected  by  a  wire  through  the  air 
;is  iii  the  ordinary  telegraph.  The  lines  that  radiate 
from  a  go  to  b.  If  a  and  b  be  4  or  5  miles  apart,  the 
earth  current  may  be  as  much  as  2  miles  broad  at  c  d, 
and  a  wire  100  feet  long  stretched  at  d  e  along  those 
lines,  and  having  its  ends  stuck  into  the  ground,  will 
have  that  part  of  the  current  travel  through  it.  If  an 
ordinary  telephone  receiver  be  connected  in  this  wire, 
any  changes  made  in  the  circuit  a  b  may  be  heard  in  the 
short  circuit  at  d.  Telegraphic  signals  may  therefore 
be  sent  to  d  from  either  a  or  b  without  any  wire  directly 


174 


NATURAL    PHILOSOPHY. 


connecting  it  with  d.     If  a  and  b  were  on  one  side  of 
a  river,  communication  could  be  made  with  d  on  the 


other  side.  The  further  apart  a  and  b  can  be  placed, 
and  the  stronger  the  current  employed,  the  greater  may 
be  the  distance  of  d  from  the  direct  wire  connecting 
the  two  stations. 

By  Induction.  —  When  the  wires  of  two  different 
circuits  are*  carried  on  the  same  poles,  as  is  the  common 
way,  the  telegraphic  or  other  currents  in  one  induce 
corresponding  currents  in  the  other,  so  that  if  the 
second  one  have  a  receiving  telephone  in  it,  all  the 
signals  may  be  heard  and  speech  transferred  from  one 
circuit  to  the  other.  Telegraphic  signals  have  been 
heard  when  the  parallel  lines  were  as  much  as  3 
miles  apart.  The  explanation  lies  in  the  fact  that  every 
current  in  a  wire  sets  up  a  magnetic  field  about  it  in 
every  direction,  as  explained  on  page  148,  and  this 
extends  to  an  indefinite  and  much  greater  distance  than 
was  imagined  before  the  telephone  was  employed  as  a 
detector.  The  facts  make  it  necessary  to  conceive 


ELECTRICITY    AND    MAGNETISM. 


175 


electric  waves  radiating  from  a  wire  carrying  vibratory 
currents,  as  they  do  from  a  vibrating  magnet,  to  im- 
mense distances,  probably  limitless,  only  growing  pres- 
ently too  weak  to  be  detected  by  present  methods. 
\Vlu-n  there  is  a  complete  metallic  circuit,  and  the 
wires  are  near  together  like  those  on  telegraph  poles, 
the  induction  effect  is  much  greater  between  them,  and 
consequently  less  strong  at  a  distance.  This  arrange- 
ment.serves  to  protect  telephone  lines  from  induction 
troubles.  If  the  telephone  line  is  itself  double,  or  a 
metallic  circuit  with  the  wires  near  together,  the  induc- 
tion effect  on  one  is  neutralized  by  an  equal  effect  on 
the  other. 

Electro-Chemical  Work.  —  It  has  already  been 
pointed  out  that  electricity  can  decompose  water,  and 
also  that  these  elements  are  not  set  free  at  the  same 
place,  but  one  at  each  of  the  terminals.  Let  the 
diagram  (Fig.  74)  represent  a  tank  containing  acidu- 


Fio.  74. 


lated  water  into  which  two  platinum  strips  dip,  and 
Ilirough  which  a  current  is  made  to  go  in  the  direction 
shown  by  the  arrow.  Oxygen  gas  will  be  set  free  at 
the  terminal  where  the  current  enters  the  liquid,  and 


176 


NATURAL    PHILOSOPHY. 


hydrogen  at  the  terminal  from  which  it  leaves  it.  By 
providing  suitable  tubes  (Fig.  75),  these  gases  may  be 
collected  and  the  quantity  measured.  It  is  found  that 
the  volume  of  hydrogen  is  twice  that  of  oxygen,  which 
corresponds  with  the  formula  for  water,  H2O>  signify- 
ing  twice  as  many  atoms  of  hydrogen  as  of  oxygen  in 
water.  If  in  place  of  water  some  chemi- 
cal solution,  such  as  sodium  sulphate,  be 
tested  in  the  same  way,  another  curious 
chemical  result  follows.  The  salt  is  de- 
composed, the  sodium  is  all  set  free  at 
one  terminal,  and  the  acid  at  the  other. 
To  observe  this  effect,  it  is  best  to  color 
the  liquid  with  purple  cabbage  solution 
(purple  cabbage  boiled  in  water).  The 
current  will  change  the  color  to  green  on 
the  sodium  side,  and  red  on  the  acid  side. 
In  this  case  it  is  the  molecule  NaOH-SO3  which  is 
decomposed  into  NaOH  and  SO3.  The  NaOH  is  an 
alkali  which  turns  vegetable  colors  to  blue  or  green,, 
while  SO3  is  an  acid  and  turns  the  same  to  red.  The 
molecules  of  the  sodium  sulphate  exchange  partners 
along  the  whole  line  of  the  current  just  as  the  water 
molecules  do  in  the  experiment  described  on  page  127. 
The  process  is  rather  slow,  unless  one  has  a  current  of 
as  much  as  an  ampere.  The  water  will  not  be  decom- 
posed appreciably  unless  the  pressure  be  as  much  as  a 
volt  and  a  half  ;  but  the  molecule  of  NaOH-SO3  will 
not  require  so  much,  that  is  to  say,  a  single  galvanic 
cell  will  suffice,  though  the  work  goes  on  slowly  with 
but  one.  Some  chemical  industries  now  employ  elec- 


FlG.  75. 


ELECTRICITY    AND   MAGNETISM.  177 

tricity  on  an  extensive  scale.  Sodium  carbonate  is  thus 
manufactured  by  decomposing  common  salt  in  a  tank 
like  that  in  Fig.  74.  The  sodium  is  set  free  at  the  H 
terminal,  and  forms  with  water  sodium  hydrate,  which 
is  alkaline.  Carbonic  acid  gas  is  driven  in  a  stream 
through  the  alkaline  solution,  and  chemical  combination 
results  in  a  solution  of  sodium  carbonate.  When  this 
is  evaporated,  the  solid  of  commerce  is  left. 

Chlorate  of  potash  is  also  manufactured  by  decom- 
posing in  a  similar  way  potassium  chloride  in  a  solution 
of  potassium  hydrate  KHO.  Chlorine  and  oxygen  are 
set  free  at  the  H  terminal,  and  these  combine  with  the 
caustic  potash  to  form  the  chlorate.  Thousands  of  tons 
of  each  of  these  products  are  made  in  this  way  every  year. 

If  a  solution  of  copper,  silver,  or  other  metalic  salt 
be  employed,  a  current  will  decompose  it  and  deposit 
the  metal  upon  the  terminal  from  which  the  current 
leaves  the  solution.  It  is  in  this  way  that  electro-plating 
is  done.  The  object  to  be  plated  is  immersed  in  a  solu- 
tion of  the  salt  of  the  metal  with  which  it  is  to  be 
covered,  and  a  plate  of  the  same  metal  is  placed  in  the 
solution.  The  current  goes  from  the  latter  to  the  former 
through  the  liquid,  and  the  dissolved  metal  is  deposited 
in  a  uniform  coating  upon  the  object.  Special  prepara- 
tions have  to  be  made,  as  the  details  for  plating  with 
silver  are  different  from  those  best  adapted  to  nickel  or 
copper  plating. 

The  amount  of  this  chemical  work  done  depends 
upon  the  strength  of  the  current  in  amperes,  as  well  as 
the  length  of  time  employed,  for  evidently  twice  as 
much  can  be  done  in  two  minutes  as  in  one  minute. 


178  NATURAL    PHILOSOPHY. 

The  weight  of  any  chemical  element  which  may  be 
set  free  from  its  chemical  combination  by  a  current  of 
one  ampere  in  one  second  —  that  is,  by  one  coulomb  of 
electricity  —  has  been  very  accurately  determined. 

As  a  coulomb  will  decompose  .001422  grains  of  water, 

.001422 

the  weight  of  hydrogen  set  free   will  be    — ~ = 

y 

.000158  grains. 

The  weight  of  other  elements  set  free  or  deposited  as 
in  plating  is  equal  to  this  weight  of  hydrogen,  .000158, 

i,.-  v    i  u    ^  •    atomic  weight 

multiplied  by  their 2 — 

valency l 

Thus,  for 

Oxygen,  .000158  X      ~  =  .001 264. 

Zinc,  «       X  ^  =  .005150. 

Copper,        «       X  ^  =  .005016. 

1  08 
Silver,  «        X^=    .01706. 

The  meaning  of  these  numbers  is  simply  that  a  current 
of  one  ampere  will  deposit  in  one  second  .01706  grains 
of  silver  upon  a  metallic  surface  exposed  to  it.  They 
also  show  that  there  is  a  quantitative  relation  between 
the  current  and  the  chemical  work  it  will  do,  and  the 
quantity  of  metal  deposited  depends  upon  the  quantity 
of  electricity  in  coulombs,  as  well  as  upon  the  atomic 
weight  of  the  metal. 

1  Valency  is  a  chemical  term  meaning  the  number  of  hydrogen  atoms  the 
given  element  is  chemically  equal  to. 


ELECTRICITY    AND    MAGNETISM.  170 

Secondary  Batteries.  —  If  the  wires  connected  to 
the  apparatus  (Fig.  74)  be  connected  to  a  galvanometer 
after  the  apparatus  has  been  decomposing  water,  the 
needle  will  show  a  current  of  electricity  which  results 
from  the  recombination  of  the  hydrogen  and  oxygen. 
Its  pressure  will  be  1.5  volts.  The  current  will  last 
no  longer  than  the  time  required  for  the  chemical  work 
due  to  the  slight  amount  of  gas  at  the  platinum  ter- 
minals. It  is  to  be  noted  that  the  terminals  are  both  of 
the  same  metal,  and  under  ordinary  conditions  no  cur- 
rent would  be  furnished.  If  two  plates  of  lead  be 
employed  instead  of  platinum,  both  immersed  in  a 
solution  of  dilute  sulphuric  acid,  and  a  current  of 
electricity  be  sent  through  them  and  the  liquid,  one 
of  them  will  be  coated  with  the  peroxide  of  lead, 
PbO2.  After  this  chemical  action  has  taken  place  the 
cell  with  its  plates  is  a  galvanic  battery,  and  can  give 
a  current  of  electricity  until  the  peroxide  is  decom- 
posed. The  cell  will  have  an  electric  pressure  of  2 
volts.  After  it  has  yielded  up  its  current  it  may  be 
again  charged  by  a  current  forming  the  peroxide  as 
before ;  then  it  will  be  ready  to  give  a  current  again. 
This  process  may  be  repeated  an  indefinite  number  of 
times.  Such  a  cell  is  called  a  secondary  battery,  and  is 
in  very  common  use  to-day.  It  is  customary  at  the 
beginning  to  apply  to  the  two  plates  of  such  a  cell  an 
artificial  coat  of  oxide  of  lead,  in  the  form  of  a  paste, 
and  then  send  the  current  through  as  before;  this 
shortens  the  process  of  formation.  The  action  of  the 
charging  current  is  not  to  charge  the  plates  with  elec- 
tricity, but  to  change  their  chemical  condition.  When 


180  NATURAL    PHILOSOPHY. 

properly  prepared,  the  two  plates  are  as  unlike  chemi- 
cally as  are  zinc  and  carbon,  and  give  a  current  of  elec- 
tricity for  precisely  the  same  reasons  so  long  as  the 
chemical  work  can  go  on.  When  the  plates  are  large, 
having  several  square  feet  surface,  they  may  receive  a 
relatively  large  amount  of  electric  energy  and  change 
it  into  chemical  energy.  They  may  yield  a  current  of 
twenty  or  thirty  amperes  for  several  hours  at  a  pressure 
of  2  volts.  The  resistance  of  such  a  cell  is  small  —  a 
few  thousandths  of  an  ohm.  To  yield  a  horse-power, 
EC  must  equal  746  watts.  If  the  current  be,  say,  25 
amperes,  then  there  must  be  Vg-  =  30  volts  nearly,  and 
this  requires  15  cells.  As  each  cell  weighs  as  much  as 
forty  pounds,  it  is  seen  that  a  battery  to  yield  a  horse- 
power would  weigh  about  six  hundred  pounds.  This 
is  one  reason  why  such  cells  have  not  been  employed 
more  extensively;  another  is  that  they  are  not  very 
durable. 

High  Electric-Pressure  Phenomena. — It  has  already 
been  said  that  an  electric  arc  consists  of  a  current  of 
electricity  between  two  separate  carbons.  It  remains 
to  be  pointed  out  that  in  electric  arc  circuits  the  carbons 
have  to  touch  each  other  in  order  to  start  the  current. 
The  current  will  not  jump  from  one  terminal  to  the 
other.  Nevertheless,  there  is  a  real  tension  at  the  car- 
bon points,  as  may  be  seen  by  attaching  a  voltmeter 
to  them ;  but  ten  thousand  volts'  pressure  is  only  suffi- 
cient to  give  a  spark  the  tenth  of  an  inch  long.  Induc- 
tion coils  are  made  capable  of  giving  pressures  of 
hundreds  of  thousands  of  volts,  and  consequently 


ELECTRICITY    AND    MAGNETISM. 


181 


much  longer  jumping  distances.  A  spark  an  inch 
long  implies  a  voltage  of  75,000,  two  inches  twice 
that,  and  so  on.  Sparks  have  been  artificially  produced 
five  feet  long ;  they  therefore  represented  between  four 
or  five  million  volts. 

Induction  coils  for  producing  sparks  several  inches 
long  (Fig.  76)  have  a  secondary  coil  of  a  great  many 
turns  of  fine  wire,  often  several  miles  long,  wound  upon  a 
spool,  which  may 
be  taken  off  of 
the  primary  coil 
and  magnet.  A 
strong  current 
of  ten  or  twenty 
amperes  in  the 
primary  coil  may 
be  interrupted 
by  hand  or  by 
some  automatic 
arrangement. 

rrn  .  J""IO.  76. 

Ihere  are  termi- 
nals to  the  secondary  which  allow  adjustment  at  dif- 
ferent distances.  The  appearance  of  the  spark  is  the 
same  as  that  of  lightning.  Its  duration  is  so  brief  that 
a  swiftly  moving  object  lighted  up  solely  l)y  the  spark 
appears  at  rest.  The  spark  may  be  made  much  brighter 
by  connecting  the  two  surfaces  of  a  Leyden  jar  to  the 
opposite  terminals  of  the  secondary  coil ;  the  spark  will 
be  shortened  to  an  inch  or  less  and  will  be  very  noisy. 

If  the  air  be  partially  exhausted  from  a  glass  tube 
three  or  four  feet  long,  the  spark  may  be  sent  through 


182 


NATURAL    PHILOSOPHY. 


it,  indicating  that  a  partial  vacuum  is  a  better  con- 
ductor than  air  at  ordinary  pressure.  Yet  if  the  air- 
pressure  be  greatly  reduced,  the  flash  will  not  pass  at 
all  through  the  tube ;  it  will  jump  three  feet  in  the  air 
rather  than  the  tenth  of  an  inch  in  the  exhausted  tube. 
This  shows  that  for  the  conduction  of  electricity  matter 
is  necessary. 

Tubes  called  Geissler's  and  Crookes'  tubes  are  made 
in  great  variety  for  showing  various  electrical  effects 


due  to  high  pressure.  In  Geissler's  the  rarefaction  is 
not  very  great,  but  the  tubes  contain  traces  of  gases  of 
different  kinds ;  each  kind  has  some  tint  different  from 
others,  and  may  in  this  way  be  studied  with  the 
spectroscope. 

In  Crookes'  tubes  the  variety  of  phenomena  is 
very  great,  ranging,  indeed,  through  a  large  part  of 
physics. 

The  mill  (Fig.  77)  has  a  wheel  which  is  made  to 
whirl  by  the  impact  of  molecules  upon  it,  as  in  the 
radiometer. 


ELECTRICITY    AND    MAGNETISM. 


183 


Tube  (Fig.  78)  has  a  platinum  disk  in  the  middle  of 
it,  and  the  impact  of  molecules  raises  the  temperature 
of  the  disk  to  a  red  heat. 

Tube  (Fig.  79)  shows  that  the  molecules  go  in  straight 


lines,  and  also  that  glass  is  fluorescent  when  bombarded 
in  this  way.  A  metallic  Greek  cross  enclosed  in  it  may 
be  raised  so  as  to  shield  the  back  of  the  glass  from  the 


molecular  shower,  and  an  image  of  the  cross  may  be 
seen  upon  the  back  of  the  glass.     When  the  glass  IKIS 


184  NATUKAL   PHILOSOPHY. 

been  lighted  a  short  time  in  this  way,  if  the  cross  be 
dropped  so  as  to  expose  the  surface  which  had  been 
protected,  and  then  the  discharges  be  repeated,  the  out- 
line of  the  cross  will  be  seen  brighter  than  where  the 
glass  had  suffered  by  the  action.  This  indicates  that 
the  glass  molecules  become  fatigued,  and  need  time  to 
recover  their  original  sensitiveness. 

Tube  (Fig.  80)  shows  how  such  electrified  molecules 
may  produce  phosphorescence.  Diamonds,  rubies,  and 

many    common 
crystals  glow  with 
^/ftfftf**  brilliancy  when 

subject    to    such 
action. 

A  magnet  held 

j  ^          near  one  of  these 

1V-  tubes  shows  that 

FIG-80-  an  electrified 

stream  of  molecules  may  be  deflected  by  a  magnetic 
field. 

All  of  these  phenomena  have  an  importance  that 
does  not  belong  to  many  otherwise  interesting  facts. 
Under  ordinary  circumstances  molecular  and  atomic 
phenomena  are  quite  invisible,  and  the  behavior  of 
molecules  has  to  be  inferred.  In  these  tubes  the  mole- 
cules are  luminous,  and  one  can  see  not  only  what  they 
do,  but  how  they  do  it.  When  the  wind  makes  the 
windmill  go  round,  one  understands  that  it  is  due  to 
the  impact  of  the  air  as  it  strikes  the  sails.  The  mill 
in  the  tube  goes  round  for  the  same  reason.  The 
metallic  terminals  within  the  tubes  are  highly  energized 


ELECTRICITY    AND    MAGNETISM.  185 

by  the  electric  pressure  to  which  they  are  subjected. 
The  gas  molecules  rebound  from  them,  not  so  much 
because  they  are  electrified  as  because  they  are  vigor- 
ously pushed  away,  as  is  the  case  with  the  radiometer 
(p.  250).  Their  velocity  is  greatly  increased,  and  they 
act  like  a  wind  blowing  upon  the  vanes  of  the  wheel. 
At  the  same  time  the  molecules  are  made  incandescent, 
and  their  direction  may  be  seen. 

When  the  bullet  strikes  the  target,  the  temperature 
of  both  is  raised,  for  mechanical  motion  has  been 
changed  into  molecular  vibratory  motion.  In  like 
manner,  in  tube  78,  the  impact  of  a  great  number  of 
molecules,  each  having  high  velocity,  act  individually, 
like  bullets,  and  heat  the  platinum  plate,  which  is  the 
target  against  which  they  strike;  and  it  is  heated  red- 
hot  if  the  energy  be  great  enough.  It  is  not  electricity 
that  heats  it ;  it  is  mechanical  impact. 

The  law  of  motion  explained  on  page  34  is  that  a 
body  in  translatory  motion  will  continue  on  in  a 
straight  line  until  some  other  body  acts  upon  it.  In 
tube  79  this  is  shown  to  be  true  of  molecules,  for  the 
sharply  defined  shadow  of  the  cross  upon  the  back 
of  the  tube  is  due  to  that  space  being  shielded  from 
impact,  and  behind  the  cross  the  space  is  dark,  while 
the  rest  is  light.  The  fatigue  of  the  molecules  already 
alluded  to  is  only  another  example  of  the  same  condi- 
tion brought  about  by  overwork  in  ordinary  matter. 
By  overwork  is  meant  making  the  matter  transform 
energy  at  a  rate  so  high  as  to  change  its  own  qualities. 
An  overworked  machine  breaks  down.  Overworked 
molecules  lose  their  elasticity. 


186  NATURAL    PHILOSOPHY. 

The  luminous  effects  in  both  gas  and  glass  indicate 
high  rates  of  vibration,  chiefly  atomic,  and  represent 
impacts  at  rates  which  compare  with  the  vibratory 
rates  of  the  atoms  themselves  ;  that  is,  are  more  or  kss 
sympathetic  (p.  281),  and  therefore  do  not  so  hastily  die 
out,  as  do  forced  vibrations.  This  phenomenon  is 
called  phosphorescence  or  fluorescence. 

The  magnetic  field,  which  may  be  shown  with  iron 
filings,  may  be  seen  to  affect  the  stream  of  shining 
molecules  in  any  of  the  tubes,  making  them  move  in 
curved  paths.  This,  is  an  ether  effect,  and  shows  that 
a  mass  of  matter  cannot  go  in  a  straight  line  through 
ether  which  is  in  a  magnetic  stress. 

STATIC   ELECTRICITY. 

There  is  another  class  of  phenomena  due  to  electric- 
ity which  are  not  ordinarily  shown  by  electrified  bodies, 
on  account  of  the  weak  effects  when  the  pressure  is  no 
more  than  a  few  hundred  volts.  When  this  reaches 
several  thousands,  phenomena  of  attraction  are  observed. 
A  glass  rod  rubbed  with  a  piece  of  silk  or  flannel  be- 
comes electrified  ;  that  is,  has  electric  pressure  devel- 
oped upon  it,  and  light  bodies  in  its  neighborhood  are 
attracted  to  it.  In  like  manner  two  strips  of  dry  brown 
paper  drawn  between  the  thumb  and  forefinger  become 
electrified  similarly,  and  repel  each  other.  If  the  hand 
be  put  between  the  loose  ends,  they  will  both  approach 
it,  and  will  recede  from  each  other  on  its  removal. 

Two  balls  a  half-inch  in  diameter,  made  of  the  pith 
of  a  sunflower  stalk,  may  be  hung  on  silk  threads  6  or 


ELECTRICITY    AND    MAGNETISM.  187 

8  inches  long,  and  serve  for  several  interesting  experi- 
ments with  electricity  developed  in  this  way.  If  the 
rubbed  glass  rod  be  brought  near  to  them  when  they 
are  suspended  as  in  Fig.  81,  they  will  both  advance  to 
meet  it  and  touch  it ;  but 
directly  they  will  leave  it, 
and  then  it  will  be  found 
that  they  are  repelled  very 
strongly  from  the  same 
rod.  Let  a  stick  of  seal- 
ing-wax be  rubbed  with 
the  same  silk,  and  brought 
near  to  the  pith  balls  that 

the  rod  repels;  they  now  will  be  attracted  by  the  stick. 
Here  are  evidences  of  two  kinds  of  electrification. 
They  are  called  positive  and  negative.  The  glass  rod 
gives  what  is  called  positive,  the  wax  negative. 

The  Electroscope  (Fig.  82)  is  a  device  for  identifying 
these  two  electrical  conditions.  It  consists  of  a  pair  of 
gold-leaf  strips  p,  3  or  4  inches  long,  connected  to  a 
metallic  stem  going  through  a  glass  tumbler  to  a  knob 
or  shelf  on  top  at  b.  The  tumbler  rests  upon  a  metallic 
support,  and  from  this  2  strips  of  tinfoil  c  and  c'  pasted 
upon  the  inside  of  the  glass  reach  into  the  tumbler  so 
the  gold  leaves  can  reach  them.  When  a  sufficiently 
electrified  body  is  brought  near  to  the  electrometer, 
the  gold  leaves  diverge.  On  removal  they  collapse. 
If  the  finger  be  touched  to  the  top  knob  while  the 
leaves  diverge,  and  be  removed  before  the  exciting  body 
is.  (hen,  removing  the  latter,  the  leaves  will  remain 


188 


NATURAL   PHILOSOPHY. 


apart.  They  are  themselves  electrified,  and  are  very 
delicate  indicators  of  the  presence  of  electrified  bodies. 
Now  electrify  the  glass  rod  as  before,  and  slowly 
bring  it  near  ;  observe  whether  the  leaves  diverge  still 
further  or  collapse.  Whichever  way  it  be,  the  excited 
stick  of  wax  will  affect  them  in  the  opposite  way.  As 
the  excited  glass  is  called  positive,  the  movement  of 
the  leaves  indicates  how  it  is  affected  by  a  positive 


charge.  Other  bodies,  such  as  books,  wood,  hard 
rubber,  crockery,  etc.,  may  be  rubbed  and  tested  in  like 
manner.  Another  experiment  is  to  rub  the  glass  with 
the  silk  as  before,  and  test  the  silk.  It  will  be  found 
negatively  electrified. 

When  two  bodies  are  rubbed  together,  and  one  of 
them  is  electrified,  the  other  one  is  oppositely  electrified. 

A  small  sheet  of  celluloid  makes  an  excellent  object 
for  observing  such  phenomena  with.  By  rubbing  it 
with  either  silk  or  woolen,  it  will  become  so  highly 
electrified  that  sparks  an  inch  long  may  be  drawn 
from  it. 


ELECTRICITY   AND   MAGNETISM.  189 

Whether  a  given  body  be  positively  or  negatively 
electrified  depends  upon  what  it  is  rubbed  with.  A 
piece  of  hard  rubber  rubbed  with  woolen  becomes 
negative  ;  if  rubbed  on  silver  it  becomes  positive  and 
the  silver  negative.  All  substances  may  be  electrified 
in  some  degree  by  friction.  Those  which  exhibit  it 
under  ordinary  conditions  are  those  called  non-con- 
ductors ;  that  is,  if  they  be  electrified  in  any  way,  the 
electricity  is  not  conducted  away.  Take  a  metallic  rod 
of  any  kind,  and  hold  it  in  a  silk  or  woolen  cloth 
wrapped  around  one  end  of  it ;  then  rub  the  free  part 
with  a  piece  of  silk  or  cat-skin,  and  test  it,  as  in  the 
other  cases,  with  the  electroscope.  It  will  be  found 
electrified.  If  it  be  held  in  the  hand  without  the 
wrapping,  —  which  is  called  insulation,  —  the  electricity 
developed  will  be  conducted  away  as  fast  as  it  appears. 
Such  phenomena  indicate  that  all  kinds  of  substances 
can  be  electrified  in  the  same  way,  and  that  such  as 
cannot  conduct  electricity  from  molecule  to  molecule 
remain  electrified.  The  molecules  of  the  surface  of 
the  glass  that  has  been  rubbed  are  all  electrified,  and 
remain  so  because  conduction  does  not  take  place. 

The  Electric  Field.  —  The  phenomenon  of  magnetic 
attraction  is  explained  as  due  to  the  magnetic  field 
which  exists  in  the  space  about  a  magnet.  Attractions 
and  repulsions  take  place  because  the  ether  pressure  is 
greater  or  less  upon  a  body  that  can  be  acted  on  by  it. 
In  like  manner  an  electrified  body  has  an  electric  field, 
within  which  all  substances  whatever  are  attracted  or 
repelled.  There  is  no  such  choice  as  there  is  with 


190 


NATURAL   PHILOSOPHY. 


magnetic  substances.  When  a  body  is  electrified  by 
rubbing  or  in  any  other  way,  it  reacts  upon  the  ether 
so  as  to  produce  a  stress  in  it,  and  in  two  different  ways, 
glass  giving  what  is  called  positive,  and  wax  negative, 
characters.  Each  one  produces  a  field  of  such  a  sort 
that  another  body  brought  into  it  becomes  electrified  in 
the  opposite  sense  ;  that  is,  a  positively  electrified  body 
induces  negative  electrification  upon  that  side  of  another 

body  which  is 
next  it,  and  posi- 
tive upon  the  re- 
mote side.  With 
small  bodies  it  is 
not  so  easy  to 
show  this  as  it  is 
with  larger  ones ; 
thus,  let  A  (Fig. 
83)  be  a  body  that  has  been  electrified  in  any  convenient 
way,  by  letting  2  or  3  electric  sparks  fall  upon  it.  Then 
if  one  end  of  an  insulated  cylinder  with  rounded  ends, 
B,  be  brought  near  to  it,  but  not  allowed  to  touch  it,  the 
cylinder  will  be  found  to  be  positively  electrified  at  one 
end,  and  negatively  at  the  other.  To  test  this,  take  a 
thin  disk  of  metal  the  size  of  a  quarter  of  a  dollar, 
fastened  to  the  end  of  a  stick  of  wax  for  a  handle  ; 
touch  the  electrified  body  A  with  this  disk,  which  is 
called  a  proof  plane ;  then  to  discover  whether  it  has 
positive  or  negative  electricity,  hold  it  near  the  excited 
electrometer.  Then  touch  the  disk  with  the  finger  to 
discharge  it,  after  which  it  may  be  touched  to  either 
end  of  the  body  B,  and  tested  in  like  manner.  This 


FIG-  ^ 


ELECTRICITY   AND   MAGNETISM.  191 

will  remind  one  of  the  magnet  which  induces  opposite 
polarity  in  a  piece  of  iron  on  the  end  next  the  pole, 
and  the  same  polarity  on  the  further  end  of  it.  A 
mechanical  idea  of  what  takes 
place  may  be  got  by  consider- 
ing the  small  ring  A  (Fig.  84) 
to  be  attached  by  spiral  springs  /  ^7  |  j^ 

on  every  side  to  a  larger  body    [ J\\\ ] 

around  it.     If  A  be  twisted  to 

the  right  or  left,  it  will  pull 

on  all  the  springs,  which  will 

all    act  to  bring  it   into   its 

normal  position  as  soon  as  it 

is  free  to  move.     If  twisted 

to  the  right,  the  springs  will  pull  to  the  left ;  and  if  it 

be  twisted  to  the  left,  they  will  pull  to  the  right.     If 

one  of  these  directions  be  called  a  positive,  the  other 

may  be  called  a  negative,  stress,  —  a  right-handed  or 

a  left-handed  twist. 

If  there  were  two  such  bodies  A  and  B  (Fig.  85),  each 
connected  by  similar  springs  about  it,  and  also  to  each 
other,  then  it  is  plain  that  if  A  were  twisted  in  either 
direction,  it  would  tend  to  twist  B  in  the  opposite  direc- 
tion. Also,  if  there  were  another  one  in  contact  with 
B  on  its  right-hand  side,  it  would  be  rotated  in  the 
same  direction  as  A.  If  A  were  right-handed,  B  would 
be  left-handed,  and  the  next  in  line  right-handed.  This 
is  only  a  mechanical  analogy  to  help  one  to  a  concep- 
tion of  what  takes  place  between  molecules  in  an  elec- 
tric field.  The  ether  that  is  about  all  bodies  holds 
their  molecules  in  certain  relative  positions,  and  when 


192  NATURAL   PHILOSOPHY. 

they  are  made  to  assume  some  new  position,  it  tends  to 
pull  them  back  ;  that  is,  the  ether  is  put  into  a  state 
of  stress  by  abnormal  positions  of  molecules,  and  another 


molecule  brought  into  that  space  is  twisted  into  an  oppo- 
site position,  which  constitute  what  is  called  the  posi- 
tive and  negative  conditions,  and  the  action  is  called 
electrical  induction. 


STATIC     ELECTRICAL    MACHINES. 

I.  Friotional.  —  By  rotating  a  piece  of  glass  against 
which  silk  or  other  substance  presses,  it  will  be  subject 
to  continuous  friction,  and  may  in  that  way  be  elec- 
trified. By  presenting  metallic  points  near  to  the  sur- 
face that  has  been  thus  electrified,  electricity  may  be 
collected  by  them,  and  the  metallic  part  to  which  the 
metallic  points  are  fixed  may  become  strongly  electrified. 
Such  a  glass  plate-machine  (Fig.  86)  works  well  in  dry 


ELECTRICITY    AND    MAGNETISM. 


193 


weather,  but  not  in  damp,  for  moisture  collects  on  the 
glass  and  other  parts  of  it.     The  electricity  is  of  very 


FIG.  86. 

high  voltage  ;  the  moisture  is  a  sufficiently  good  con- 
ductor for  electricity,  so  it  leaks  away  and  cannot  be 
accumulated. 

IT.  Inductive.  —  There  are  several  kinds  of  machines 
which  depend  upon  inductive  action  ;  that  is,  some 
part  is  electrified  at  first,  and  its  inductive  action  upon 
the  glass  plate  or  plates  which  may  be  rotated  serves 
to  keep  them  electrified ;  and  by  means  of  the  metallic 
points,  electricity  is  collected  as  in  the  frictional 
machines.  The  action  of  such  machines  is  complicated. 
Some  of  them  need  to  be  separately  excited,  others  are 
self-excited,  and  most  of  them  are  less  affected  by 
dampness  than  the  frictional  machines.  With  such  a 


194  NATURAL   PHILOSOPHY. 

machine  (Fig.    87)    in    good    order,  having   plates  20 
inches  in  diameter,  one  may  get  sparks  4  or  5  inches 


long,  and  many  interesting  experiments  may  be  made 
with  such  high-pressure  electricity. 


STORAGE. 

The  Leyden  Jar.  —  This  consists  of  a  glass  jar 
(Fig.  88)  coated  inside  and  out,  nearly  to  the  mouth  of 
the  jar,  with  tinfoil  pasted  on  it.  Through  the  cork  is 
a  metallic  conductor  with  a  chain  touching  the  inner 
foil,  and  ending  at  the  top  with  a  ball.  If  such  a  jar  be 
held  in  the  hand  while  the  knob  is  touched  to  one  of 
the  knobs  of  the  electric  machine  while  the  latter  is 
worked,  the  jar  will  become  charged.  It  will  contain 
electricity  in  what  is  called  its  static  form,  and  will 
retain  it  for  a  long  time  if  pains  be  taken  to  prevent 


ELECTRICITY    AND    MAGNETISM.  195 

its  discharge.  Such  a  charged  jar  may  be  discharged 
by  connecting  the  inner  and  outer  surface  by  any  con- 
ductor. The  knuckle  will  do,  but  it  is  likely  to  give 
one  a  shock,  so  a  device  called  a  discharger 
is  employed;  it  consists  of  metallic  arms 
with  a  glass  handle  (Fig.  89).  One  may 
touch  with  safety  either  the  knob  alone  or 
the  outer  surface  alone  of  the  jar ;  so  it  is 
entirely  safe  to  hold  it  in  the  hand  while 
charging  it. 

The  charge  resides  upon  the  glass  and  not 
upon  the  metallic  coating.     This  is  shown  by 
making  the  jar  in  separable  parts  :    thus  a 
glass  goblet  (Fig.  90)  fitting  into  a  tin  cup  that  serves 
for  the  outer  coating,  a  smaller  tin  cup  fitting  into  the 

glass  for  the  inner  coat- 
ing.  A  glass  tube  extends 
from  the  bottom  of  this 

FIG.  89.  ., 

inner  jar  to  the  knob  on 

the  end,  to  enable  one  to  take  it  out  without  discharg- 
ing it.  When  all  are  in  place  it  may  be  charged  by 
holding  the  metallic  outer  cup  in  the  hand,  and  holding 
the  knob  from  the  inner  cup  to  the  electrifying  machine 
until  the  jar  is  heard  to  hiss.  Then,  after  setting  it 
upon  the  table,  remove  the  inner  jar  D  by  taking  hold 
of  the  glass  tube,  after  which  it  may  be  handled  all 
over  with  safety ;  then  the  glass  B  may  be  removed  and 
set  by  itself  ;  the  outer  cup  C  will  then  remain,  and 
this,  too,  may  be  handled  like  any  tin  cup.  If  they  be 
put  together  again  as  at  A,  the  whole  may  be  discharged 
with  a  snapping  spark  with  the  discharger  as  at  first. 


196  NATURAL    PHILOSOPHY. 

Now  let  the  same  jar  be  charged  and  taken  apart  as 
before.  With  the  electrometer  and  proof  plane  (p.  190), 
test  the  two  surfaces  of  the  glass  ;  they  will  be  found 
to  be  oppositely  electrified.  If  the  hand  be  put  into 
the  glass  without  touching  it,  a  crackling  sound  will 
be  heard,  and  a  sensation  as  if  the  hand  were  in  a 
spider's  web  will  be  felt. 

These  are  most  interesting  facts,  as  they  have  directly 
to  do  with  electrical  theory.  The  two  sides  of  the 
glass,  being  oppositely  electrified,  are  in  an  opposite 

state  of  strain. 
The  molecules 
are  twisted  into 
new  positions, 

and    tllis    condi- 
tion  is  slowly  con- 

FIG-90-  ducted   through 

from  one  side  to  the  other,  so  it  is  not  possible  to 
wholly  discharge  the  glass  at  once.  Charge  it  in  the 
common  way,  let  it  stand  for  five  minutes,  then  dis- 
charge it.  Let  it  remain  for  a  minute  or  two,  and 
another  spark  may  be  got  from  it.  This  shows  that 
electrification  is  an  affair  of  the  glass  molecules,  and 
takes  time  for  their  action.  If  a  wooden  twig  be 
twisted  half-way  round  and  then  freed,  it  will  fly  back 
most  of  the  way  to  its  normal  position  at  once  ;  but 
the  original  position  will  not  be  reached  for  an  appre- 
ciable time.  If  it  be  highly  elastic,  it  will  vibrate  for 
a  short  time  to  and  fro,  twisting  in  each  direction 
alternately.  This  is  precisely  what  happens  in  the  dis- 
charge of  the  jar  ;  the  electric  current  is  not  simply 


ELECTRICITY    AND    MAGNETISM. 


197 


a  spark  in  one  direction,  but  an  alternating  current, 
the  period  depending  upon  the  size  of  the  jar.  The 
latter,  in  discharging,  acts  like  an  elastic  body,  giving 
currents  in  both  directions,  and  setting  up  ether  waves 
having  a  length  that  depends  upon  the  number  of 
vibrations  of  the  coating  of  the  jar,  just  as  the  length 
of  sound  waves  in  air  depends  upon  the  number  of 
vibrations  of  the  body  that  produces  them.  For  a 
gallon  jar  this  number  is  hundreds  of  millions  per 
second ;  so  the  wave-length  may  be  a  few  feet  long,  for 
ether  waves  move  at  the  rate  of  186,000  miles  a  second, 
no  matter  how  they  originate  or  what  their  wave-length. 
Every  charged  body  is  to  be  considered  as  having  its 
molecules  in  a  state  of  strain,  and  every  spark  of  dis- 
charge as  relieving  the  strain,  and  producing  vibrations 
like  elastic  bodies. 

Metallic  Points  discharge  electricity  into  the  air 
without  a  spark. 

A  spherical  body  like  a  cannon  ball  or  a  bullet  may 
be  electrified,  and  retain  its  charge  for  a  long  time  if  it 


FIG.  91. 


198  NATURAL    PHILOSOPHY. 

be  perfectly  insulated,  so  that  the  electricity  cannot 
creep  away  on  the  support ;  but  if  it  be  provided  with 
a  point,  it  will  be  discharged  almost  instantly  into  the 
air.  In  like  manner,  if  a  point  like  that  of  a  darning- 
needle  be  presented  to  a  charged  body  (Fig.  91),  it  will 
discharge  itself  through  the  needle  without  the  noisy 
spark  which  otherwise  would  be  produced. 

There  is  a  mechanical  reaction  between  the  air  and 
the  point  from  which  electricity  is  escaping,  as  is  shown 
by  mounting  a  number  of  pointed  wires  so  they  may 
rotate  (Fig.  91).  It  will  also  blow  upon  a  candle  flame, 
and  a  strong  discharge  may  extinguish  the  flame. 

All  of  the  experiments  which  may  be  performed 
with  the  induction  coil  (p.  181)  may  be  shown  with 
electricity  developed  with  static  machines.  Indeed, 
there  is  no  difference  except  in  the  degree  and  manner 
of  generation. 

Lightning  is  a  phenomenon  of  electricity  of  exceed- 
ingly high  pressure  or  voltage.  It  originates  in  clouds 
when  condensation  is  taking  place  at  a  rate  too  high 
for  the  energy  to  be  radiated  away  by  the  ordinary 
process.  The  frequent  formation  of  hail  as  an  accom- 
paniment to  thunder  showers  shows  that  the  changes 
are  very  rapid.  When  the  electric  tension  between  the 
cloud  and  the  earth  exceeds  75,000  volts  to  the  inch, 
there  is  a  discharge  from  the  one  to  the  other  through 
some  air  path  which  cannot  be  foreseen,  for  the  tem- 
perature of  the  air,  the  amount  of  moisture,  dust,  and 
gases  present  are  varying  all  the  time.  When  such 
clouds  are  high,  that  is,  half  a  mile  or  more,  the  light- 


ELECTRICITY    AND    MAGNETISM.  199 

ning  discharges  go  from  one  cloud  to  another  ;  when 
less  than  that  distance,  the  discharge  is  more  frequently 
into  the  earth,  generally  by  the  way  of  a  tree  having 
roots  that  spread  near  a  water  course,  or  a  damp  locality 
that  acts  as  a  conductor  from  the  cloud  to  the  mass  of 
the  earth.  The  form  of  a  flash 
of  lightning  is  not  zigzag,  as 
has  so  often  been  pictured,  but 
is  rather  a  wavy  line  (Fig.  92), 
as  is  the  spark  seen  from  an 
induction  coil.  Its  course  is 
partly  determined  by  the  pres- 
ence of  dust  particles  along  its 
line.  There  is  no  evidence 
that  it  has  momentum. 

Flashes  between  clouds  are 
of  very  short  duration,  gener- 
ally less  than  the  hundred- 
thousandth  of  a  second  ;  but 
some  discharges  to  the  earth 
last  a  second  or  more,  and 
represent  a  great  amount  of  energy,  as  is  seen  by  the 
destruction  they  sometimes  cause.  It  has  been  shown 
that  some  discharges  are  as  great  as  250  coulombs. 

Protection  from  Lightning.  —  As  trees  are  liable 
to  be  struck  by  lightning,  they  are  unsafe  places  for 
shelter  in  a  thunder  shower.  It  is  wiser  to  take  a 
drenching  than  to  seek  the  protection  of  trees.  For  the 
protection  of  houses  it  has  long  been  the  custom  to 
attach  metallic  rods  to  the  outside,  with  branches  raised 


200  NATURAL   PHILOSOPHY. 

above  the  tops  of  chimneys  and  other  higher  points. 
The  lower  ends  are  carried  into  a  well,  moist  earth,  (tr 
connected  to  metallic  water  or  gas-pipes,  so  as  to  con- 
vey any  accidental  discharge  into  the  earth.  Such  rods 
are  useful,  but  many  buildings  have  been  struck  when 
provided  with  them  in  the  most  approved  manner.  It 
is  rare  that  any  one  is  seriously  injured  in  a  house  thus 
defended,  though  sometimes  the  house  itself  is  injured. 
Lightning  and  other  high  voltage  alternating  currents 
are  easily  interrupted  in  ordinary  conductors  and  find 
new  paths.  They  seldom  keep  entirely  to  the  wire  or 
rod  provided  for  them.  It  is  now  deemed  safer  to 
employ  flat  straps  of  iron  or  copper  stretched  along  the 
ridge  pole  and  down  the  roof  angles  and  each  corner  of 
the  house  to  the  ground,  so  as  to  have  a  kind  of  coarse 
net  over  the  house,  the  lower  end  being  carried  into 
the  ground  as  before.  Similar  straps  should  be  carried 
up  the  outer  parts  of  the  chimneys,  and  fastened  around 
them  at  the  top. 

Iron  gas-pipe  an  inch  in  diameter  is  as  good  as  any- 
thing for  such  purposes,  and  it  has  the  advantage  of 
being  cheap  and  readily  adjustable  to  any  length. 
Platinum-tipped  forks  for  the  top  of  the  rods  are  of  no 
special  value,  and  insulators  are  useless. 

Conclusion  as  to  the  Nature  of   Electricity.  —  It 

is  plain  that  whenever  electricity  is  generated,  some 
mechanical,  chemical,  or  heat  phenomena  are  its  ante- 
cedents, that  is,  movements  of  masses  of  matter  of 
some  degree  of  magnitude.  If  they  are  movements  of 
large  masses  of  matter  that  may  be  seen,  we  call  the 


ELECTRICITY    AND    MAGNETISM.  201 

phenomena  mechanical ;  4f  they  are  too  minute  to  be 
'seen,  we  call  them  molecular  phenomena  ;  but  the  pres- 
ence of  matter,  and  some  of  its  motions  are  indispensa- 
ble. Also,  when  electricity  does  work  of  any  kind,  — 
turning  a  motor,  decomposing  molecules,  heating  a 
mass  of  matter,  or  giving  light,  —  it  is  giving  motion  of 
one  kind  or  another  to  the  matter  it  acts  upon,  or  it 
produces  a  pressure  in  it  when  it  cannot  move  it,  as 
when  one  presses  with  his  hand  against  the  wall.  The 
amount  of  matter  is  not  changed  in  any  degree  by  any 
process.  The  only  change  taking  place  in  any  phe- 
nomenon is  a  change  of  motion  of  one  kind  or  another, 
mechanical  or  molecular  in  matter,  and  stress  or  vibra- 
tions in  the  ether,  and  these  motions  are  exchangeable 
with  each  other  under  proper  conditions. 

There  is  no  known  phenomenon  in  the  ether  which 
does  not  depend  upon  the  prior  action  of  matter  to  pro- 
duce it.  It  follows  that  electricity  is  a  phenomenon  of 
molecules  in  which  energy  is  in  a  different  form  from 
its  common  mechanical  or  heat  form.  The  mechanical 
is  known  as  translatory,  the  heat  as  vibratory  ;  and  the 
probability  is  very  strong  that  electricity  represents 
rotary  motions  among  molecules  and  atoms.^ 


QUESTIONS. 

1.  If  a  wire  has  a  resistance  of  10  ohms  to  the  mile,  what 
will  be  the  resistance  of  250  miles  of  the  same  kind  of  wire? 

2.  If  a  pound  of  No.  10  copper  wire  has  a  resistance  of  .033 
of  an  ohm,  what  will  be  the  resistance  of  115  pounds  of  it? 

3.  A  thousand  feet  of  No.  25  copper  wire  has  a  resistance  of 
33  ohms  ;  what  will  be  the  resistance  of  a  mile  of  it  ? 


202  NATURAL    PHILOSOPHY. 

4.  If  1000  feet  of  No.  10  wire  Ijas  a  resistance  of  1  ohm,  what 
will  be  the  resistance  of  the  same  length  of  wire  which  has  twice 
the  diameter? 

5.  What  will  be   the  resistance  of   the  same  length  if   the 
diameter  be  one-half? 

0.    What  will  be  the  resistance  of  iron  wire  in  each  of  the 
above  cases  if  copper  be  six  times  better  than  iron  as  a  conductor'.' 

7.  No.  40  copper  wire  has  a  resistance  of  1  ohm  to  the  foot ; 
what  is  the  resistance  per  foot  of  iron,  platinum,  and  carbon  fila- 
ment, if  of  the  same  diameter  as  the  copper  ? 

8.  What  will  be  the  electro-motive  force  of  10  ammonium 
chloride  battery  cells  if  they  are  connected  in  series? 

9.  If  a  cell  have  an  electro-motive  force  of  2  volts,  and  a 
resistance  of  1  ohm,  what  current  will  it  give  through  a  wire  so 
short  and  large  that  its  resistance  is  too  small  to  take  account  of  ? 

10.  What  current  will  the  cell  give  through  a  wire  with  9 
ohms'  resistance  ? 

31.  A  cell  having  an  E.  M.  F.  of  1.4  volts  will  give  what  cur- 
rent through  the  circuit  of  an  electro-magnet  having  a  resistance 
of  5  ohms,  its  own  resistance  being  .5  of  an  ohm  ? 

12.  A  battery  cell  is  giving  a  current  of  1  ampere  when  the 
resistance  is  known  to  be  2  ohms ;  what  is  the  E.  M.  F.  of  the  cell? 

33.  What  is  the  resistance  of  a  circuit  when  a  battery  with  1.8 
volts  gives  a  current  of  3  amperes  ? 

14.  A  telegraph  sounder  requires  .1  of  an  ampere  to  work  it 
properly  ;  if  a  battery  of  4  cells,  each  with  1.5  volts,  be  in  series 
in  the  circuit,  what  must  be  the  resistance  of  the  circuit  that  it 
may  be  worked  ? 

15.  A  telegraph  wire  200  miles  long  has  a  resistance  of  10  ohms 
to  the  mile  ;  with  a  galvanic  battery  having  an  E.  M.  F.  of  150 
volts  and  an  internal  resistance  of  100  ohms,  how  much  current 
will  be  in  the  circuit  if  the  grounds  at  the  ends  have  100  ohms 
each?     Suppose  there   be  5  relays  in  the  circuit,  each  with  150 
ohms'  resistance  ;  how  much  current  will  now  traverse  the  circuit? 

16.  An  incandescent  electric  lamp  is  lighted  by  a  current  of  1 
ampere,  and  the  pressure  is  100  volts  ;  what  is  the  resistance  of 
the  lamp? 


ELECTRICITY    AND    MAGNETISM.  203 

17.  If  there  be  fifty  such  lamps  arranged  in  multiple  order  in 
a  circuit,  how  many  amperes  must  be  sent  into  the  wires  that 
lead  to  the  lamps  ? 

18.  How  many  watts  are  spent  in  a  lamp  taking  50  volts  and 
1.2  amperes? 

19.  How  many  watts  are  there  to  10  electrical  horse-power? 

20.  How  many  watts  are  spent  in  an  incandescent  electric  light 
circuit,  with  110  volts  and  100  lamps,  each  taking  .6  of  an  ampere? 
What  electrical  horse-power  is  spent  in  the  lamps? 

21.  If  a  battery  cell  having  2  volts'  pressure  furnishes  a  cur- 
rent of  2  amperes,  what  part  of  a  horse-power  does  it  yield? 

22.  How  many  foot-pounds  of  work  can  the  same  cell  do  in  1 
second?     In  an  hour? 

23.  What  current  must  be  furnished  by  a  battery  of  25  two- 
volt  cells  in  order  to  produce  a  horse-power? 

24.  If  a  carriage  requires  2  horse-power  to  drive  it,  and  its 
motor  takes  20  amperes,  how  many  two-volt  cells  will  be  needed? 

25.  An  arc-light  circuit  has  90  lamps  in  series  in  it.     Each 
lamp  requires  45  volts  and  5  amperes  to  run  it ;  how  many  elec- 
trical horse-power  are  spent  in  them  ? 

26.  What  will  be  the  resistance  of  each  lamp  on  the  above 
supposition  ? 


CHAPTER  X. 

ETHER     WAVES. 

Origin  of.  —  In  the  chapter  on  heat  it  is  explained 
how  heat  originates  from  mechanical  sources  such  as 
percussion,  friction,  and  condensation,  from  chemical 
sources  such  as  combustion,  and  from  electrical  cur- 
rents ;  also  how  heat  is  transferred  by  the  mechanical 
processes  of  conduction  and  convection  from  one  body 
to  another.  There  is  still  another  way  by  which  heat 
energy  may  be  transferred  from  one  body  to  another 
without  the  bodies  being  in  contact,  that  is,  without 
conduction. 

If  a  cannon  ball  were  heated  to  a  red  heat  and  hung 
by  a  wire  from  the  ceiling,  it  would  lose  its  tempera- 
ture slowly,  and  one  in  its  presence  could  feel  the 
warmth  from  it  upon  his  hands  and  face.  A  little 
attention  will  show  that  this  is  not  due  to  the  heated 
air  that  is  all  about  it,  for  air  currents  will  not  be  felt 
except  over  it,  and  a  glass  put  between  the  hand  and 
the  hot  ball  will  stop  air  currents,  but  not  the  sensa- 
tion. A  hot  body  will  cool  almost  as  freely  in  the 
most  perfect  vacuum  that  can  be  made  as  it  will  in 
free  air,  as  is  shown  by  the  incandescent  electric  lamp 
which  has  a  red-hot  filament  of  carbon  in  a  vacuum. 
When  the  current  is  stopped,  the  filament  becomes  black 
and  cools  almost  instantly.  Conduction  is  out  of  the 


ETHER    WAVES.  205 

question,  and  the  energy  represented  by  the  high  tem- 
perature finds  another  way  of  escape. 

Again,  that  which  we  call  light,  whether  from  fire 
or  sun  or  stars,  gets  to  us  in  some  way  from  bodies  at 
all  distances  from  us.  Hold  the  hand  in  sunlight  and 
warmth  may  be  felt ;  yet  we  are  confident  that  between 
the  sun  and  the  earth  there  is  a  space  of  93,000,000 
miles  in  which  there  is  a  more  perfect  vacuum  than 
one  can  possibly  produce  in  any  artificial  way.  Energy 
gets  to  us  across  this  space  void  of  matter. 

On  page  138  the  omnipresent  ether  is  mentioned, 
and  the  properties  of  magiiets  and  of  electric  currents 


are  explained  as  due  to  its  action.  Here  again  it  must 
be  considered  as  the  agency  by  which  heat  energy  is 
transferred  from  one  body  to  another. 

The  atoms  and  molecules  of  all  bodies  are  extremely 
minute  (p.  7)  and  elastic  (p.  16).  When  they  possess 
much  energy  and  collide  with  each  other  vigorously, 
they  vibrate  like  bells  or  other  sounding  bodies,  and 
thereby  set  up  waves  in  the  ether  which  travel  in  every 
direction,  as  in  Fig.  93  ;  and  these  waves  continue  to 
travel  on  in  straight  lines  until  they  come  to  another 
mass  of  matter,  as  at  b,  which  may  stop  them  or  turn 
tin-in  in  some  new  direction.  If  the  body  b  stops  these 
waves,  itself  becomes  heated  by  them,  and  its  molecules 


206  NATURAL   PHILOSOPHY. 

vibrate  like  a,  that  is,  the  temperature  of  b  rises.  The 
waves  thus  produced  in  the  ether,  by  vibrating  mole- 
cules, are  called  ether  waves,  and  the  energy  they  repre- 
sent is  sometimes  called  radiant  energy,  because  it  is 
radiated  from  a  hot  or  vibrating  body. 

Consider  now  what  has  mechanically  happened  as 
illustrated  in  Fig.  93,  where  a  represents  an  atom  or 
molecule  of  ordinary  matter  in  a  state  of  vibration  ; 
that  is,  is  heated,  has  some  temperature.  It  is  sur- 
rounded with  ether,  and  every  vibration  does  work  on 
the  ether,  producing  a  disturbance  in  it  which  assumes 
the  form  of  a  wave  ;  and  a  series  of  vibrations  cause  a 
series  of  waves  which  follow  each  other.  What  was  at 
first  a  vibratory  motion  of  matter  has  now  become  a 
wave  motion  in  the  ether ;  the  energy  which  at  first 
was  called  heat  energy  has  now  become  radiant  energy. 
There  has  been  a  transference  of  it  from  one  body  to 
another,  and  a  transformation  from  one  kind  to  an- 
other ;  hence  it  is  no  longer  proper  to  speak  of  the 
energy  of  the  ether  waves  as  heat  energy  ;  its  only 
name  now  is  radiant  energy.  When  these  waves  fall 
upon  other  molecules,  as  at  b,  the  energy  is  changed 
back  to  its  vibratory  or  heat  form.  Thus  by  two  trans- 
formations is  heat  transferred  from  one  body  to  another 
by  means  of  the  ether,  irrespective  of  distance. 

Velocity  of  Ether  Waves.  —  The  ripples  made  by 
dropping  a  stone  in  water  move  with  a  velocity  that 
depends  upon  the  property  of  the  water  to  transmit 
waves,  not  upon  the  manner  in  which  the  waves  are 
made.  Likewise  the  waves  set  up  in  the  ether  in  any 


ETHER    WAVES.  207 

manner  travel  through  it  with  a  velocity  that  depends 
upon  the  properties  of  the  ether.  That  they  travel 
much  faster  than  sound  waves  travel  is  plain,  because 
one  can  see  the  light  from  a  cannon  or  from  fireworks 
some  time  before  the  sound  of  the  explosion  is  heard. 
How  fast  ether  waves  or  light  does  travel  has  been 
measured  in  a  number  of  ways.  One  of  them  is  by 
means  of  the  motions  of  the  satellites  of  the  planet 
Jupiter.  The  satellites  move  about  the  planet  with 
great  regularity,  and  the  time  it  takes  for  one  revolu- 


FIG.  94. 

tion  is  very  accurately  known.  In  the  figure  94  let  S 
represent  the  sun,  B  and  B'  the  earth  in  opposite  parts 
of  its  orbit,  and  J  the  planet  Jupiter,  and  one  of  its 
satellites  in  its  orbit.  When  the  earth  is  at  B',  it  is 
farther  away  from  Jupiter  than  when  at  B  by  the  diam- 
eter of  the  orbit  of  the  earth,  which  is  twice  the  dis- 
tance of  the  sun  from  the  earth, —  93,000000  X  2  = 
186,000000  miles.  The  eclipse  of  the  satellite  is  seen 
to  take  place  1000  seconds  later  at  B'  than  at  B,  which 
shows  that  it  takes  the  light  that  length  of  time  to  go 
from  B  to  B';  that  is,  it  goes  at  the  rate  of  186,000 
miles  a  second  through  the  ether,  and  a  little  slower 
through  air,  water,  glass,  and  other  transparent  bodies. 
This  very  great  speed  of  light  or  radiant  energy  will 


208  NATURAL   PHILOSOPHY. 

help  one  to  conceive  the  vastness  of  the  visible  universe. 
Above  and  around  the  earth  in  every  direction  the 
stars  are  to  be  seen  at  night.  It  is  the  business  of  the 
astronomer  to  measure  the  distances  to  these  luminous 
points,  and  he  tells  us  the  nearest  of  the  fixed  stars  is 
so  far  away  that  it  requires  three  and  a  half  years  for 
its  light  to  reach  the  earth.  Others  are  so  remote  that 
thousands  of  years  are  required.  The  light  we  now 
see  from  them  left  them  before  the  Christian  era  began, 
before  Rome  was  founded,  or  the  pyramids  were  built , 
and  if  such  a  distant  star  were  to  be  annihilated  to-day, 
it  would  continue  to  shine  upon  us  for  thousands  of 
years. 

Wave-Lengths.  —  It  has  been  found  possible  to 
measure  the  length  of  the  waves  that  affect  our  eyes. 
Different  colors  have  different  wave-lengths,  as  in  the 
following  table  : 

Red,  the  thirty-seven  thousandth  of  an  inch. 

Orange,  "  forty-two  «  "  "  " 

Yellow,  "  forty-five  "  "  "  " 

Green,  "  forty-eight  "  "  "  " 

Blue,  "  fifty-three  "  "  "  " 

Violet,  «  sixty-three  «  «  "  " 

Lavender,  "  sixty-five  "  "  "  " 

There  are  waves  longer  and  shorter  than  these,  but 
the  eye  is  affected  only  by  those  within  the  above 
limits. 

Number  of  Vibrations.  —  One  may  compute  the 
number  of  times  the  molecule  vibrates  per  second  when 
the  velocity  of  the  waves  is  known,  and  their  length  ; 


ETHER    WAVES.  209 

for,  let  v  represent  the  velocity,  I  wave-length,  n  num- 
ber of  vibrations  :  n  =  — .      If  I  be  the  wave-length  for 

red  waves  =  ^Y^o  of  an  inch,  then  n  will  be  the  num- 
ber of  times  -5^-$-$  of  an  inch  is  contained  in  186,000 
miles,  which  is  about  400  millions  of  millions  of  times, 
and  for  waves  g?{,^  of  an  inch  long,  about  750  mil- 
lions of  millions.  A  pocket  tuning-fork  may  vibrate. 
522  times  a  second ;  the  shortest  piano-string,  4000 
times  ;  the  highest  sound  that  can  be  heard  is  made  by 
bodies  vibrating  25,000  times  ;  but  these  are  hardly  to 
be  compared  with  the  amazing  number  of  vibrations 
made  by  atoms  and  molecules  when  they  produce 
ether  waves.  The  smaller  a  body  is,  the  higher  is  its 
rate  of  vibration.  A  tuning-fork  the  fifty-millionth  of 
an  inch  in  length,  if  made  of  steel,  would  vibrate  about 
30,000  millions  of  times  a  second  ;  if  it  were  made  of 
ether  instead  of  steel,  its  rate  of  vibration  would  be 
greater  in  the  proportion  that  the  velocity  of  movement 
in  ether  is  greater  than  that 
in  steel,  which  is  about  50,- 
000  times. 

50,000  X  30000,000000 
=  1,500,000,000,000,000,  a 
number  which  shows  that  the 
vibratory  motions  of  mole- 
cules, as  determined  by  their 

wave-lengths,  are  such  as  would  be  expected  of  such 
minute  bodies  if  they  were  made  of  ether. 

The  ether  waves  we  call  light  are  to  be  thought  of 
as  traceable  back  in  every  case  to  molecules  and  atoms 


210 


NATURAL    PHILOSOPHY. 


that  are  in  a  true  state  of  vibration  ;  not  oscillations 
to  and  fro,  but  changes  of  form  such  as  a  ring  of  brass 
or  steel  wire  5  or  6  inches  in  diameter  would  make  if 
plucked  (Fig.  95). 

Phenomena  of  Ether  Waves.  —  A  line  of  waves 
like  a  b  (Fig.  93)  is  called  a  ray.1  A  bundle  of  rays  is 
called  a  beam.  The  rays  from  a  candle  or  other  source 
of  such  waves  may  be  seen  from  every  direction  in  an 
apartment,  and  every  part  of  the  flame  may  be  seen, 
so  every  part  of  the  flame  must  be  giving  out  rays  in 
every  direction. 

A  beam  may  consist  of  parallel,  converging,  or  diverg- 
ing rays.  Hold  a  convex  lens  in  the  sunshine,  and  the 


rays  will  be  converged  to  a  point  from  which  they  will 
diverge.  If  this  be  tried  in  a  darkened  room  with  a 
beam  of  sunshine  directed  into  the  room  by  a  mirror 
outside  (Fig.  96),  the  direction  of  the  beam  may  easily 

1  The  definition  of  a  ray  as  here  given  is  only  a  convenient  term  to  indicate 
the  direction  of  the  forwanl  movement  of  other  waves.  In  reality  there  are  710 
more  such  individual  things  as  light  rays  than  there  are  water  rays  when  a 
pebble  is  thrown  into  water,  and  waves  travel  out  in  all  directions  on  the  sur- 
face. A  line  drawn  radially  from  the  center  of  disturbance  would  go  through 
all  the  waves,  and  the  waves  would  travel  through  the  line  prolonged.  Such  a 
line  might  be  called  a  ray. 


KTIIKI:     \VAVKS.  211 

be  seen  by  means  of  the  dust  particles  in  the  air.  A 
little  chalk-dust  serves  well  to  show  the  character  of  the 
beam.  Before  the  beam  enters  the  lens,  it  is  parallel; 
after  passing  through,  it  is  converged  to  a  point  beyond 
which  it  diverges.  The  point  of  light  in  front  of  the  lens 
may  be  used  as  a  luminous  point,  and  objects  held  be- 
t  \\veu  it  and  the  wall  will  have  sharply  denned  shadows. 
The  shape  of  the  shadows  shows  that  the  rays  go  in 
stratyltt  lim-x;  otherwise  the  shadows  would  be  irregular. 
If  the  source  of  light  has  considerable  area,  the  edge  of 
the  shadow  cast  by  it  will  not  be  as  dark  as  the  middle 
of  the  shadow.  Hold  an  object  like  a  ball  in  the  light 
of  a  candle  or  lamp,  as  in  Fig.  97,  and  observe  the 


FIG.  97. 

character  of  the  shadow.  The  light  from  the  tip  of  the 
flame  casts  its  shadow  from  a  to  d ;  the  light  from  the 
base  f  gives  its  shadow  from  c  to  b.  Between  a  and 
c,  b  and  d  some  rays  fall,  but  none  between  a  and  b. 
The  part  a  b  is  called  the  umbra,  or  complete  shadow ; 
the  other  is  called  the  penumbra,  or  partial  shadow. 
The  shadows  of  objects  in  the  sunshine  are  never  well 


212  NATURAL    PHILOSOPHY. 

defined ;  the  luminous  surface  of  the  sun  is  so  large 
there  is  always  a  penumbra. 

If  the  shutters  or  the  curtains  of  a  room  be  drawn  so 
as  to  exclude  most  of  the  light,  and  an  aperture  half 
an  inch  in  diameter  be  made  in  one  of  the  shutters,  a 
picture  of  the  whole  landscape  will  be  visible  upon  the 
walls  and  ceiling  of  the  room.  By  holding  a  sheet  of 
white  paper  2  or  3  feet  away  from  the  aperture,  most  of 
the  prominent  outside  objects 
will  be  recognizable,  every- 
thing in  its  proper  place  and 
color,  but  all  inverted.  This 
effect  is  finest  in  winter  when 
snow  covers  the  ground,  as 
so  much  more  light  is  re- 
flected from  snow  than  from  grass  or  common  objects. 
The  image  is  inverted  because  the  light  rays  all  go 
in  straight  lines,  as  indicated  in  Fig.  98. 

Brightness  of  Illumination.  —  If  a  certain  amount 
of  light  from  a  point  falls  upon  an  area  of  a  square  foot 
at  any  distance  from  the  point,  the  surface  will  have  a 
certain  degree  of  brightness.  If  it  be  removed  to  twice 
its  original  distance,  only  one-fourth  as  much  light  will 
now  fall  upon  it,  for  the  same  amount  of  light  will 
be  spread  over  four  times  the  surface.  This  follows 
because  light  moves  in  straight  lines  (Fig.  99).  The 
brightness  will  therefore  be  but  one-fourth  the  bright- 
ness of  the  surface  in  the  first  position. 

This  is  sometimes  expressed  by  saying  that  the  in- 
tensity of  light  varies  inversely  as  the  square  of  the 


ETHKK    WAVES. 


'213 


distance  from  the  source.  The  relative  brightness  of 
two  sources  of  light  may  be  measured  by  observing  the 
difference  in  the  density  of  the  shadows  produced  by 
each  (Fig.  100).  The  shadows  of  the  post  upon  the 
screen  surface  may  be  made 
to  fall  side  by  side  by  moving 
one  or  the  other  sources  of 
light.  By  moving  either  of 
them  towards  or  away  from 
the  post,  a  place  may  be  found 
where  the  two  shadows  are  ap- 
parently alike.  If  the  distance  from  the  screen  to  each 
source  be  now  measured,  the  relative  brightness  of  the 
sources  will  be  as  the  square  of  their  distances.  Suppose 
a  candle  be  placed  1  foot  away  from  the  screen,  and  a 
lamp  is  found  to  give  an  equal  shadow  at  the  distance  of 
4  feet ;  then  the  latter  will  be  as  many  times  brighter 


FIG.  99. 


than  the  other  as  the  square  of  4  is  greater  than  the 
square  of  1  ;  that  is,  the  lamp  gives  a  light  equal  to 
16  candles.  Such  a  device  is  called  a  photometer.  The 
standard  of  brightness  is  commonly  that  of  a  sperm 
candle  burning  120  grains  an  hour.  The  common 


214  NATURAL    PHILOSOPHY. 

paraffine  candle  differs  but  little  from  this.  A  lamp 
that  gives  10  times  as  much  light  as  this  standard 
candle  is  said  to  be  of  10  candle-power. 

The  following  table  gives  the  relative  brightness  of 
several  common  sources  of  light: 

Standard  candle,                                1  candle-power. 

Kerosene,  Rochester  lamp,             25  "  " 

Gas  jet,  12  to  18  "  » 

Gas,  Welsbach  burner,  30  to  50  "  " 

Oxyhydrogen  lime  light,               200  "  " 

Electric  arc,  common,                   800  "  " 

Electric  arc  search-light,     1,000,000  or  more      "  " 

The  sun  does  not  much  differ  in  brightness  from  the 
electric  arc,  which  is  the  brightest  that  can  be  pro- 
duced artificially. 

Brightness  and  amount  of  light  are  different  things. 
A  spark  may  be  brighter  than  a  candle  flame,  but  the 
latter  gives  more  light  because  its  shining  area  is 
greater.  The  moon  gives  much  light  because  it  is 
so  large.  The  part  of  an  electric  arc  which  is  brightest 
is  rarely  more  than  the  tenth  of  an  inch  square  ;  but  if 
the  surface  of  the  sun  were  covered  with  such  bright 
spots,  it  would  give  nearly  as  much  light  as  we  now  get 
from  it. 

In  these  and  all  other  sources  of  light  depending 
upon  combustion,  there  are  chemical  actions  taking 
place,  and  atoms  are  recombining  into  new  molecules. 
Whenever  this  happens,  the  atoms  are  vigorously  shaken 
and  vibrate  with  great  energy.  This  energy  they  lose 
by  radiation.  When  a  current  of  electricity  produces 
light  in  a  carbon  filament,  the  carbon  molecules  are 


ETHKi;    WAVES.  215 

highly  heated  and  therefore  vibrate  ;  they,  too,  lose  their 
energy  by  producing  ether  waves,  the  energy  of  the 
waves  being  equal  to  the  energy  supplied,  else  the 
temperature  of  the  lamp  would  not  remain  uniform. 

Action  of  Matter  upon  Ether  Waves. — When  ether 
waves  meet  a  mass  of  matter  they  are  either  reflected, 
absorbed,  or  transmitted;  usually  all  three  happen  in 
some  degree,  depending  upon  the  kind  of  matter  and 
its  condition. 

When  the  direction  of  the  rays  is  changed,  as  when 
a  ray  of  sunlight  ab  (Fig.  101)  falls  upon  a  mirror,  the 
rays  b  c  are  said  to  be  reflected. 
A  ray  or  a  beam  which  falls 
upon  any  surface  whatever  is 
called  an  incident  ray  or  beam. 
Thus  ab  (Fig.  101)  is  an  inci- 
dent ray;  b  c  is  a  reflected  ray. 

If  a  line  b  d  be  drawn  per- 
pendicular to  the  surface  of 
the  mirror  at  the  point  b  where 

the  ray  meets  it,  then  the  angles  abd  and  dbc  are 
equal;  abd  is  called  the  angle  of  incidence,  and  dbc  is 
called  the  angle  of  reflection.  These  angles  are  both 
in  the  same  plane.  Let  the  mirror  be  tilted  so  the 
reflected  ray  will  be  directed  back  towards  a,  then  d 
will  also  be  in  the  same  line.  If  the  mirror  be  tilted 
forty-five  degrees,  the  ray  of  light  will  have  moved 
ninety  degrees,  and  in  general  the  ray  will  move 
through  twice  the  angle  the  mirror  moves  through. 

If  in  a  darkened  room  a  small  beam  of  sunlight  be 


216  NATURAL   PHILOSOPHY. 

admitted  from  a  mirror  outside,  and  a  mirror  be  held  in 
its  path,  it  will  have  its  direction  changed,  and  may  be 
traced  through  the  air  to  the  wall.  If  a  piece  of  white 
paper  or  other  light-colored  object  be  put  in  the  path 
of  the  beam,  it  will  reflect  light  to  every  part  of  the 
room.  The  difference  in  action  of  the  glass  and  the 

paper  is  due  to  the  dif- 
ference in  the  character 
of  the  surfaces  of  the 
two  bodies,  the  glass 
being  smooth  and  even, 
the  other  very  uneven 
(Fig.  102).  A  common 
magnifier  will  show  that 
the  surface  of  the  paper 

is  rough,  so  that  the  individual  rays  meet  it  at  different 
angles,  where  each  follows  the  above  law  of  reflection. 

A  piece  of  clear  glass  or  mica  will  allow  such  a  beam 
of  light  to  go  through  it  without  much  loss ;  but  some 
of  the  rays  will  be  reflected  to  the  wall,  and  the  amount 
of  these  so  reflected  depends  upon  the  angle  the  glass 
presents  to  the  beam  If  the  beam  be  perpendicular  to 
the  surface,  the  least  amount  will  be  thus  reflected.  If 
the  beam  meets  the  surface  at  a  large  incident  angle, 
nearly  all  the  light  will  be  reflected  and  but  little  trans- 
mitted. A  body  that  permits  light  to  go  through  it  so 
that  objects  may  be  plainly  seen  through  it  like  common 
window  glass  is  called  a  transparent  body.  One  that 
scatters  the  light  that  goes  through  it  like  paper  or 
roughened  glass  is  called  a  translucent  body;  and  one 
that  prevents  all  light  from  going  through  is  called  an 


ETHER    WAVES.  217 

opaque  body.  If  the  opaque  body  have  a  dark  and  rough- 
ened surface,  like  a  blackboard,  but  little  light  will  be 
reflected  from  it.  The  light  will  be  absorbed ;  as  radiant 
energy  it  will  be  changed  back  into  heat,  and  the  tem- 
perature of  the  opaque  body  will  rise.  The  warmth 
felt  upon  the  face  and  hands  when  exposed  to  sunshine 
or  the  light  from  a  fire  shows  this,  and  many  objects 
become  uncomfortably  hot  when  left  in  the  sunshine 
for  a  time,  because  they  have  absorbed  the  energy  of 
the  ether  waves  that  have  fallen  upon  them.  A  per- 
fectly transparent  body  would  not  get  thus  heated,  for 
if  the  ether  waves  were  transmitted,  their  energy  would 
not  be  left  behind. 

A  piece  of  clear  glass  or  a  quantity  of  clear  water 
becomes  warm  when  exposed  to  sunshine  or  firelight, 
which  shows  that  they  are  not  transparent  for  all  waves. 
The  clearest  lamp  chimneys  stop  about  ten  per  cent  of 
the  light  which  falls  upon  them  ;  and  at  the  depth  of 
one  hundred  feet  in  clear  water  it  is  dark,  though  the 
sun  may  be  shining  vertically  into  the  water.  All  the 
light  and  all  the  energy,  except  what  is  reflected  at  the 
surface,  is  absorbed.  If  there  were  a  body  which  would 
absorb  all  waves,  it  could  not  be  seen  unless  it  were 
self-luminous.  The  black- 
board absorbs  more  light 
than  chalk  absorbs. 


Multiple  Reflection. 


,  .    ,  ,  FIG.  103. 

Light  or  ether  waves  are 

reflected  in  some  degree  from  every  surface  they  meet. 

A  piece  of  plane  glass  held  in  the  sunlight  reflects  from 


218  NATUllAL   PHILOSOPHY. 

its  front  surface  much  of  the  light  falling  upon  it.  If 
the  back  of  the  glass  is  covered  with  mercury  or  silver, 
we  have  what  we  call  a  looking-glass,  which  reflects 
nearly  all  the  light,  but  the  light  is  reflected  from  the 
second  surface.  If  a  piece  of  thick  plate  glass  be  held 
so  a  small  beam  of  light  half  an  inch  in  diameter  can  fall 
obliquely  upon  it,  a  number  of  reflections  can  be  seen  on 

the  wall,  caused 
by  the  reflections 
back  and  forth 

/  X^XX^         through  the  glass 

m  at  tne   surface 

(Fig.  104).  These 

are  called  multiple  reflections.  The  thicker  the  glass,  the 
farther  apart  these  will  be ;  and  the  greater  the  angle  of 
inclination  of  the  beam,  the  brighter  the  reflections  will 
appear,  as  a  larger  amount  of  light  is  reflected  at  each 
surface.  In  looking  into  a  plate-glass  mirror  one  may 
sometimes  see  a  faint  double  image  of  himself,  the 
fainter  one  being  the  reflection  from  the  front  surface 
of  the  glass. 

MIRRORS. 

I.  Plane.  —  An  object  seen  by  reflection  from  a 
mirror  appears  as  far  behind  the  mirror  as  the  object 
is  in  front  of  it.  If  the  object  be  seen  by  reflected 
light,  then  the  light  which  comes  to  the  eye  must  have 
been  reflected  from  the  surface  of  the  mirror  at  such 
points  as  lie  between  the  eye  and  the  image  as  seen. 
The  position  of  the  image  and  the  direction  in  which  it 
is  seen  may  be  drawn  correctly  by  first  drawing  the  parts 


ETHER    WAVES. 


219 


of  the  image  as  far  behind  the  mirror  M  (Fig.  105)  as 

they  are  front  of  it,  as  at  i,  then  drawing  lines  from  the 

extremities  of  the  image 

i  to  the  eye  e.      These 

two   lines   represent   the 

direction  of  the   rays  of 

light  after  reflection  from 

the  mirror.     If  lines  now 

l)e  drawn  from  the  extrem- 

-  .    .  FIG.  105. 

ities  of  o  to  these  points 

on  the  mirror,  they  will  represent  the  direction  of  the 
rays  upon  the  mirror  which  are  reflected  to  the  eye  at 
e.  Other  eyes  at  a  or  b  would  still  see  the  image  i  in 
the  same  position,  but  different  rays  from  o  would  be 
reflected  from  different  points  on  M,  and  would  be  drawn 
in  same  way  without  change  of  position  of  the  image. 

II.  Curved  Mirrors. — Reflecting  surfaces  may  also 
be  made  concave  or  convex ;  but  whether  the  one  or  the 
other,  the  law  of  reflection  holds  true  for  them.  There 
may  be  any  number  of  kinds  of  curved  surfaces.  Let  a  b 

(Fig.  106)  represent  a 
concave  mirror,  —  a  part 
of  a  spherical  surface,— 
I"  with  c  as  the  center  of 
^Vi  curvature.  Suppose  that 
b  at  c  there  were  a  source 
of  light  so  that  radiations 
would  travel  in  every  direction  from  it.  Any  rays. 
ce,  ch,  or  cl,  would  meet  the  surface  of  ab  at  right 
angles  to  it,  for  these  lines  are  radii  ;  these  rays  ami 


\, 


Fie.  KIC. 


220  NATURAL   PHILOSOPHY. 

all  others  would  be  reflected  back  to  c.  Suppose  a  ray 
from  some  other  source  and  direction  as  mh  strike  the 
mirror  at  h.  It  will  be  reflected  so  that  the  angle  of 
incidence  equals  the  angle  of  reflection  ;  mhc  is  the 
angle  of  incidence,  for  ch  is  at  right  angles  to  ab. 
Draw  chf  =  mlic;  hf  represents  the  direction  of  the 
reflected  ray.  It  crosses  the  line  d  e  at  f.  In  like 
manner  the  ray  nl  is  reflected  to  the  same  point  on 
line  de.  All  parallel  rays  will  be  reflected  to  this  same 
point  f,  which  is  half-way  distant  from  the  mirror  to  its 
center  of  curvature.  This  point  is  called  the  principal 
focus  of  the  mirror  ;  that  is,  it 
is  the  focus  for  parallel  rays. 
If  now  a  source  of  light  were 
to  be  placed  at  f,  the  light 
would  be  reflected  in  a  beam 
parallel  to  d  e,  and  would  travel 

FIG.  1OT. 

on   to  an   indefinite   distance. 

The  axis  of  this  beam  d  e  is  called  the  principal  axis  of 
the  mirror.  Let  another  ray  start  from  some  other  point 
on  this  axis  as  at  p  (Fig.  106),  and  fall  on  the  mirror  at 
some  point,  say  at  h.  The  angle  phc  would  be  less 
than  mhc  of  Fig.  107  ;  hence  the  reflected  ray  would 
cross  ce  at  p',  between  f  and  c,  and  the  closer  p  is  to 
c,  the  nearer  will  the  reflected  ray  be  to  c,  until  points 
p  and  p'  coincide  with  c.  A  source  of  light  at  p'  will  l>e 
reflected  to  p;  hence  p  and  p'  are  called  conjugate  foci. 

Images    Produced    by    Coii<'av<»     >Iirrors.  —  If    a 

candle  flame  be  brought  up  near  the  principal  focus  of 
a  concave  mirror,  a  place  may  be  found  by  trial  where 


ETHER   WAVES.  221 

the  image  of  the  flame  may  be  seen  upon  the  opposite 
wall.  It  will  be  inverted  and  enlarged.  If  without 
moving  the  mirror  the  flame  be  carried  to  the  wall 
where  its  image  appeared,  and  a  small  piece  of  white 
pa  PIT  be  put  where  the  candle  was,  a  small  inverted 
image  of  the  candle  will  appear  upon  the  paper.  These 
points  represent  the  conjugate  foci  mentioned  above. 
A  diagram  showing  how  these  effects  can  be  made  may 
be  drawn  as  follows :  Let  a  b  (Fig.  108)  represent  an  object 


FIG.  ins. 

at  any  distance  from  the  mirror  m  n  beyond  the  center  c. 
Light  from  every  portion  of  the  object  falls  on  eveiy 
part  of  the  mirror.  A  ray  ac  through  the  center  of 
curvature  of  the  mirror  will  be  reflected  back  in  the 
same  line  ;  likewise  the  ray  b  c.  Draw  a  line  from  a  to 
any  part  of  the  mirror  as  to  h.  The  reflected  my  will 
cross  the  first  ray,  which  goes  through  the  center  of 
curvature  at  a',  and  all  rays  from  a  will  be  reflected  to 
this  same  place  below  the  axis.  This  will  be  the  focus 
for  the  point  of  the  arrow.  From  b  draw  a  line  to  any 
part  of  the  mirror  as  to  1,  making  the  angle  of  inci- 
dence equal  to  the  angle  of  reflection;  the  reflected 


222 


NATURAL   PHILOSOPHY. 


Fio.  109. 


ray  will  cross  the  line  through  b  and  c  at  b',  and  con- 
sequently the  heel  of  the  reflected  arrow  will  be  above 
the  axis,  and  the  image  of  the  intermediate  parts  of 
ab  will  be  between  these  two  fixed  points.  The  image 
will  be  inverted  and  smaller  than  the  object. 

An  object  ab  placed  between  the  center  of  curvature 
and  the  mirror  has  an  enlarged  image  a'  b'  apparently 

behind  the  mirror. 
The  position  and 
proportional  size  of 
this  image  may  be 
determined  by 
drawing  lines  from 
the  center  of  cur- 
vature C  past  the 
extremities  of  the 
object  a  b,  and  prolonging  them  behind  the  mirror.  Lines 
drawn  from  the  same  points  of  ab,  and  made  parallel 
with  the  axis,  will  meet  the  mirror  at  c  and  d,  and 
other  lines  drawn  from  the  focus  f,  half-way  between 
the  center  of  curvature  and  the  mirror,  through  the 
points  c  and  d,  and  prolonged  until  they  meet  the  first 
lines,  will  give  the  position  of  the  image  a'  b'.  It  is  to 
be  kept  in  mind  that  the  parallel  rays  ac  and  bd  will 
be  reflected  to  f ,  as  if  they  had  come  from  a'  b'.  Ob- 
jects looked  at  in  a  convex  mirror  appear  diminished 
in  size,  for  ab  and  a'  b'  are  conjugate;  that  is,  either 
may  be  the  image  of  the  other. 

Refraction.  —  When  a  small  beam  of  light  is  directed 
into  water  or  a  piece  of  glass  at  any  angle  except  a 
right  angle,  the  beam  is  observed  to  be  bent  from  its 


ETHER    WAVES.  223 

original  course,  becoming  more  nearly  perpendicular. 
Thus  the  beam  a  on  reaching  the  glass  is  partly  reflected 
from  the  front  surface,  as  indicated  by  the  arrow,  and 
partly  transmitted  through  the  glass  in  a  new  direction. 
On  reaching  the  opposite  surface  it  is  again  bent  into 
its  original  direction,  provided  the  sides  of  the  glass 
are  parallel.  This  change  in  the  direction  of  light  on 
entering  a  new  medium  is  called 
refraction,  and  the  power  of  refrac- 
tion is  possessed  in  some  degree 
by  all  transparent  bodies,  whether 


solids,  liquids,  or  gases.  _/ 

The  new  direction  given  to  any  / 

ray  is  determined  at  the  surface  of  the 
new  medium,  and  does  not  change 
so  long  as  the  substance  remains  uniform  in  density  and 
constitution,  the  ray  continues  to  move  in  a  straight 
line  through  it.  If  the  substance  does  change  in  either 
density  or  composition,  the  ray  is  at  once  refracted  more 
or  less.  Thus  the  light  coming  from  the  sun  or  a  star 
has  to  traverse  the  thickness  of  the  atmosphere,  which 
is  denser  the  nearer  it  is  to  the  surface  of  the  earth. 
The  refractive  power  becomes  greater  and  greater,  so 
the  real  course  of  all  rays  except  those  coming  verti- 
cally down,  is  a  curved  line,  being  more  and  more 
deflected.  In  the  atmosphere  this  curvature  is  at  a 
maximum  when  the  source  of  light  is  at  the  horizon, 
and  is  sufficient  then  to  tilt  the  ray  downward  half  a 
degree,  which  is  equal  to  the  diameter  of  the  sun  or 
moon.  It  follows  that  either  of  these  luminaries  may 
lu>  seen  when  they  are  really  below  the  horizon. 


224 


NATURAL   PHILOSOPHY. 


The  Law  of  Refraction.  —  For  a  given  substance  like 
water  or  a  piece  of  glass,  it  is  found  that  the  change  in 
the  direction  of  a  ray  of  light  may  be  known  when  the 
angle  acb  (Fig.  Ill)  at  which  it  meets  the  surface  is 
known  ;  a  c  b  is  the  angle  of  incidence,  e  c  d  is  the  angle 
of  refraction.  Describe  a  circle  with  c  as  a  center,  and 
from  points  on  the  circumference  where  a  c  and  c  e  cross 
it,  draw  lines  perpendicular  to  bd,  that  is,  if  and  eh. 

These  lines  represent 
the  sines  of  the  angle 
of  incidence  and  of  re- 

.  sine  acb 
traction,  and  — — 

sine  e  c  d 

is  the  same  whatever 
the  value  of  acb;  it 
is,  therefore,  a  constant 
quantity  and  called  the 
index  of  refraction.  If 
the  light  goes  from  air  into  water,  the  value  of  this 
index  is  ^  ;  if  from  air  to  glass,  •§-. 

There  is  another  meaning  to  these  figures :  they  indi- 
cate the  relative  rates  at  which  light  travels  in  the  sub- 
stances. Thus,  if  light  travels  in  air  at  the  rate  of 
185,000  miles  a  second  (a  thousand  miles  a  second  less 
than  in  free  space),  it  travels  but  three-fourths  as  fast 
in  water  and  two-thirds  as  fast  in  glass.  This  has  been 
proved  by  experiment. 

How  Light  becomes  Refracted.  —  As  light  is  a 
wave  motion,  it  may  be  mechanically  represented  by 
shaking  rapidly  the  end  of  a  long,  limp  rope  ;  the 


FIG.  ill. 


ETHER    WAVES. 


225 


wave  would  travel  along  it,  but  the  movement  of  each 
point  on  the  rope  is  a  to-and-fro  motion  at  right  angles 
to  the  direction  of  the  wave,  the  same  as  the  movement 
of  the  hand  that  starts  the  wave.  In  a  free  medium 
the  direction  of  such  a  wave  is  always  at  right  angles  to 
the  direction  of  the  vibration  ;  it  is  the  latter  that  deter- 
mines the  direction  of  forward  movement.  Suppose  a  b 
represents  the  direction  of  march  of  a  platoon  of  soldiers 
d  e,  keeping  their  front  at  right  angles  to  their  direction 
of  march.  So 
long  as  there  is 
no  obstruction 
at  any  part  of 
the  way,  they 

will    all    move  

with  uniform 
velocity.  If  they 
should  come  to 

more  difficult 

FIG.  112. 
ground    h  d,    at 

an  angle  where  the  rate  of  march  would  be  retarded, 
d  would  meet  it  first.  When  the  middle  of  the 
platoon  b  had  reached  the  same  ground,  d  would 
not  have  been  able  to  travel  as  far,  but  would  have 
gone  to  g;  when  h  reached  the  same  ground,  d  would 
have  got  only  to  f,  and  df  is  shorter  than  eh.  The 
frontage  of  the  whole  body  would  have  been  changed 
to  a  new  direction,  and  if  the  direction  of  march  was  to 
be  perpendicular  to  the  platoon,  it  would  now  go  towards 
c;  there  would  have  been  refraction.  In  similar  way, 
if  the  line  of  march  were  revei-sed  from  c  towards  b,  h 


226  NATURAL   PHILOSOPHY. 

would  get  out  soonest,  and  the  whole  body  would  be 
swung  round  to  face  a,  and  the  rate  of  advance  would  be 
quickened.  For  such  reasons  the  direction  a  ray  of  light 

takes  on  entering  a 
new  medium  depends 
upon  the  angle  at 
which  it  meets  the 
new  medium  and 
upon  density. 

If  a  ray  be  made 
incident  upon  a  tri- 
angular piece  of  glass 

riu.  11.5.  11      *•  •  ,TT 

called  a  prism  (Fig. 

113),  it  will  be  bent  still  more  from  its  original  direc- 
tion on  leaving  the  prism,  as  indicated  by  the  arrows. 
Another  prism  inverted  will  direct  another  ray  across 
the  first  at  C.  If  instead  of  flat-faced  prisms  the  glass 
be  made  with  curved  surfaces  (Fig.  114),  parallel  rays 
will  all  be  brought  to  the  same  point  f,  which  is  called 


a.  focus,  and  the  glass  with  such  a  curved  surface  is  called 
a  lens.  Of  course  there  may  be  any  degree  of  curvature, 
and  it  may  be  convex  or  concave.  A  lens  with  only 


ETHER    WAVES.  227 

one  side  curved  is  called  a  plano-convex  or  plano-concave 
lens,  as  the  curvi-d  surface  is  convex  or  concave.  If 
both  sides  are  curved,  it  may  be  double  convex  as  1  in 
Fig.  114,  or  double  concave,  or  one  face  convex,  the 
other  concave,  and  is  then  called  a  meniscus. 

Properties  of  Lenses.  —  A  line  drawn  through  the 
center  of  a  lens  as  P  P'  is  called  its  axis,  and  the  focus 
of  a  lens  is  somewhere  along  this  axis.  Kays  parallel 
to  this  axis  as  a  and  b  come  to  a  focus  at  some  point 
on  this  axis  as  f,  which  is  called  the  principal  focus  of 
the  lens.  The  focal  length  of  the  lens  is  the  distance 


from  the  middle  of  the  lens  C  to  the  principal  focus. 
The  focal  length  of  the  lens  may  be  measured  by  hold- 
ing the  lens  in  the  sunshine  so  as  to  focus  the  rays 
upon  a  piece  of  paper,  and  then  measuring  its  distance 
from  the  lens  ;  or  in  a  darkened  room  hold  the  lens  so 
an  image  of  a  distant  object,  like  a  tree  or  a  steeple  a 
mile  away,  may  be  plainly  seen  on  a  piece  of  white 
paper,  then  measure  the  distance  from  paper  to  lens. 
Nearer  objects  will  give  a  different  and  larger  value. 
Thus  if  P  be  a  source  of  light,  rays  from  it  falling  on 
the  lens  will  be  brought  to  a  focus  at  P',  further  away 
than  the  principal  focus.  Also,  if  a  source  of  light  be 
placed  at  P',  the  rays  will  come  to  a  focus  at  P.  These 


228  NATURAL    PHILOSOPHY. 

two  points  so  exchangeable  with  each  other  are  called 
conjugate  foci.  Any  change  in  the  position  of  one  pro- 
duces a  corresponding  change  in  the  other.  There  is 
a  definite  relation  between  the  principal  focus  and  the 
conjugate  foci  of  a  lens,  represented  by  the  expression 

-  -J-  —  =  7.,  where  P  and  P'  are  the  conjugate  foci  and  f 

the  principal  focus  ;  so  if  one  knows  two  of  these 
factors,  he  may  compute  the  other. 

Images  Formed  by  L.CIIS.  —  Place  a  lens  between  a 
lighted  candle  or  lamp  and  the  wall  where  an  image  may 
be  formed  (Fig.  116).  By  moving  either  the  lens  or  the 


light  along  the  axis  of  the  lens,  a  point  will  be  found 
by  trial  where  an  enlarged  and  inverted  image  of  the 
flame  will  be  seen  upon  the  wall.  This  may  be  under- 
stood by  remembering  that  for  every  point  on  ab  there 
is  a  conjugate  focus  at  a'  b'.  The  rays  from  point  a, 
which  fall  on  the  lens,  will  be  brought  to  a  focus  at  a'. 
The  lines  in  the  figure  are  made  heavier  in  order  to 
make  this  plain.  In  like  manner  all  the  rays  from  b 
will  be  focused  at  b'.  All  points  between  a  and  b  will 
have  corresponding  points  between  a'  and  b'.  But  a'  is 


ETHER    WAVES. 


229 


below  the  axis  while  a  is  above  it.  The  distance  of  a' 
from  the  axis  is  also  greater  than  the  distance  of  a  from 
it;  that  is,  the  image  is  larger  —  is  magnified.  If  the 
distance  from  ab  to  the  lens  be  known,  as  well  as 
the  focal  length  of  the  lens,  the  distance  to  the  screen 
at  a'  b'  can  be  computed.  Thus  suppose  focal  length 
of  lens  be  one  foot,  the  distance  of  ab  from  lens  14 
inches  ;  how  far  away  is  the  image  ? 

-  4-  -7  =  -        r-r  4-  -  =  TT        x  =  7  feet= distance 
p  '  p'      J        14^  x       12 

of  the  inverted  image. 

This  use  of  the  lens  is  very  common,  and  is  called 
projecting.     Either  sunlight,  lime  light,  or  electric  light 


Fro.  117. 

may  be  used.  For  sunlight  a  mirror  M  is  fixed  in  the 
window  so  as  to  direct  a  beam  of  sunlight  into  the 
room  onto  a  screen.  This  is  called  a  porte-lumiere.  A 
double  convex  lens  o,  four  or  five  inches  in  diameter 
and  about  a  foot  focus,  answers  well.  This  placed  in 
the  path  of  the  beam  serves  to  give  a  disk  of  light  on 
the  screen.  The  size  of  the  disk  depends  only  upon  its 
distance  away  from  the  lens.  Any  object  placed  about 
a  foot  back  from  the  lens  will  show  an  enlarged  image 
on  the  screen,  and  transparencies  made  for  such  purpose 


230 


NATURAL   PHILOSOPHY. 


placed  there  will  give  bright  and  pleasing  pictures, 
better  than  can  be  produced  by  the  electric  light.  A 
lens  used  for  this  purpose  is  called,  an  objective.  For 
still  better  definition  than  such  a  single  lens  can  give, 
objectives  are  sometimes  made  compound. 

By  drawing  the  lines  to  indicate  the  direction  of  rays 
from  a  lens,  it  will  be  seen  that  the  shorter  the  focus  of 
the  lens,  the  more  the  light  will  be  dispersed,  and  con- 
sequently the  less  bright  will  a  picture  be.  To  make  it 
brighter,  more  light  must  be  used.  This  is  effected  by 
using  a  lens  as  a  light  condenser.  An  object  at  a  (Fig. 
118)  has  more  light  upon  it  than  it  would  have  had 
nearer  the  lens  c,  which  when  thus  used  is  called  the 


condenser.  The  short  focus  objective  o  magnifies  the 
object  very  much  and  enables  one  to  see  microscopic 
things,  such  as  vinegar  eels,  by  placing  them  in  a  glass 
tank  and  holding  it  at  a.  A  plate  of  glass  placed  there, 
having  a  small  drop  of  solution  of  sal  ammoniac  rubbed 


ETHER    WAVES. 


231 


on  it,  will  finely  show  the  process  of  crystallization. 
This  device  is  called  the  solar  microscope. 

The  Lens  as  a  Magnifier.  —  If  one  looks  through  a 
convex  lens  at  an  object  nearer  to  the  lens  than  its 
focus  is,  the  object  appears  enlarged.  Let  ab  be  an 


FIG.  119. 

object.  To  an  eye  at  E  its  magnitude  would  be  meas- 
ured by  the  angle  aEb,  which  is  called  the  visual  angle. 
If  a  lens  1  be  placed  between  the  object  and  the  eye, 
the  ray  al  will  be  refracted  to  the  eye  at  E,  and  will 
make  the  point  of  the  arrow  seem  to  be  in  the  direction 
of  El;  the  same  for  the  rays  from  the  heel  of  the 
arrow.  This  makes  the  visual  angle  a'  E  b'  much  wider 
ai id  the  object  looked  at  appear  much  bigger  and  nearer; 
that  is,  it  has  been  magnified.  Such  a  lens  is  called  a 
simple  microscope. 

The  Compound  Microscope. — To  see  minute  objects 
a  small,  short  focus  lens  is  needed.  As  it  cannot  be 
brought  near  enough  to  the  eye  to  conveniently  see 
with  it,  it  is  used  in  combination  with  another  and 


232 


NATURAL   PHILOSOPHY. 


larger  lens.     The  smaller  lens  o  next  to  the  object  a  b 
forms  an  image  of  the  latter  at  some  point  as  at  cd. 


The  same  rays  pass  on  .to  the  larger  lens  1,  called  the 
eye  piece,  and  by  this  they  are  refracted  to  the  eye, 
making  a  much  wider  visual  angle  than  there  could 
have  been  otherwise,  and  ab  is 
seen  amplified  to  a'b'. 

For  convenience  these  lenses  are 
mounted  in  tubes  capable  of  ad- 
justment (Fig.  121).  The  objec- 
tive o  of  a  microscope  is  generally 
compound,  and  its  focal  length  is 
generally  less  than  an  inch,  and 
may  be  as  short  as  one-tenth  or  one- 
twentieth,  but  satisfactory  work 
cannot  be  done  with  such  short 
ones.  A  good  microscope  may 
enable  one  to  see  an  object  as 
small  as  a  hundred-thousandth  of 
an  inch  in  diameter.  The  magnify- 
ing power  of  a  microscope  is  generally  stated  in  diam- 
eters, that  is,  as  100  or  500  diameters.  An  object  T^¥ 


FIG.  121. 
Compound  Microscope. 


KTHKIi    WAVKS. 


233 


of  an  inch  long  in  actual  measure  would  appear  to  be 
one  inch  long  if  magnified  100  diameters. 

If  the  diameter  of  a  molecule  of  water  be  the  fifty- 
millionth  of  an  inch,  and  the  best  microscope  of  to-day 
will  show  nothing  finer  Hum  the  hundred-thousandth 
of  an  inch,  then  in  order  to  see  the  molecule  it  is 
needful  to  make  the  microscope  as  many  times  better 
than  we  now  have  it  as  100,000  is  contained  in 
50,000,000,  which  is  500  times.  Then  the  molecule 
would  appear  simply  as  a  point  without  parts.  But 
motions  of  a  body  are  magnified  as  much  as  their  parts, 
and  if  molecules  be  in  incessant  motion,  as  their  phe- 
nomena indicate,  they  could  not  be  seen  if  the  micro- 
scope were  otherwise  able  to  show  it.  Hence  there  is 
no  probability  of  one's  ever  being  able  to  see  such  a 
molecule. 

The  Telescope.  —  The  telescope  is  a  combination  of 
two  or  more  lenses  to  enable  one  to  see  distant  objects 
more  plainly,  viz.,  a  large  lens  o  (Fig.  122)  for  forming 


an  image  of  a  distant  object  at  its  focus,  and  a  smaller 
lens  for  the  eye  piece  E,  to  receive  and  again  refract  these 
rays  to  the  eye  ;  the  image  is  enlarged  to  a  degree  that 
depends  upon  the  magnifying  power  of  the  eye  piece 
E.  The  image  is  inverted  as  already  explained.  For 
looking  at  the  stars  this  makes  no  difference,  so  for  an 


234  NATURAL    PHILOSOPHY. 

astronomical  telescope  these  two  lenses  only  are  neces- 
sary. The  larger  the  objective,  the  more  light  reaches 
the  eye,  and  the  better  a  faint  and  distant  object  can  be 
seen. 

The  greater  the  diameter  of  the  objective,  the  longer 
is  its  focal  length  and  the  tube  needed  for  its  use.  An 
objective  36  inches  in  diameter  needs  a  tube  60  feet 
long,  and  the  40-inch  objective  for  the  Yerkes  telescope 
at  Chicago  has  a  tube  nearly  70  feet  long.  Only  about 
2000  stars  can  be  seen  on  a  clear  night  by  the  eye  alone ; 
but  in  the  whole  sky  as  many  as  a  hundred  millions  can 
be  seen  with  the  large  glasses,  and  each  increase  in  the 
size  of  these  glasses  reveals  other  stars  beyond  in  every 
direction. 

The  Spy  Glass.  —  When  two  glasses  are  used  the 
image  seen  is  always  inverted.  This  renders  it  unserv- 
iceable for  common  use.  By  employing  two  more 
glasses  the  image  is  again  inverted,  thus  bringing  it  to 
a  proper  position ;  and  so  a  spy  glass  is  provided  with 
four  glasses,  the  first  pair  for  magnifying,  the  second 
pair  for  giving  an  erect  image,  —  all  mounted  in  an  ad- 
justable tube  for  proper  focusing  for  objects  at  different 
distances. 

Prismatic  Refraction.  —  When  a  beam  of  sunlight 
is  sent  through  a  triangular  prism  so  as  to  be  refracted, 
it  is  noticed  that  the  beam  leaves  the  prism,  not  colorless 
as  it  entered,  but  as  a  band  of  colored  lights  (Fig.  123), 
which  show  upon  the  wall  as  a  series  of  rainbow  tints 
in  which  as  many  as  six  distinct  colors  may  be  counted, 
—  red,  orange,  yellow,  green,  blue,  and  violet.  The  red 


ETHER    WAVES.  235 

is  least  refracted  while  the  violet  is  most  refracted.  If 
a  similar  prism  be  held  in  either  of  these  colored  rays, 
the  rays  will  be  still  more 
refracted,  but  none  of 
them  will  be  broken  up 
into  other  colors.  These 
colors  in  this  order  are 
known  as  the  spectmm. 
The  same  series  of  colors 
may  be  seen  by  letting 
light  from  any  common 

source  of  light,  as  a  candle,  gas-jet,  or  an  electric  light, 
pass  through  a  prism.  If  now  a  second  prism  be  placed 
against  the  first  prism  so  all  the  light  will  have  to  pass 
through  it  also  (Fig.  124),  the  whole  beam  will  be  re- 
I'raeted  back  to  the  straight  line  it  would  take  if  no  prisms 
were  in  its  path,  and  the  colors  will  disappear,  leaving  a 
white  spot  upon  the  wall  opposite  the  window.  These 
experiments  show  that  white  light  from  whatever  source 
is  compound,  and  the  prism  serves  to  separate  the  con- 
stituents, which  may  be  again  reunited  into  white  light. 
In  various  ways  the  rays  of  these  colors  have  had  their 

wave-lengths  measured, 
f\       y  ;i  i id  some  of  the  measure- 

NT"/  "    ments  are  given  on  page 

208.    By  comparing  the 
FIG.  124.  .  ,  PI 

positions  of  the  tints  in 

the  spectrum  with  these  numbers,  it  will  be  seen  that 
tin'  shorter  the  WV//VK.  flu'  tnon-  tln'if  are  refracted.  This 
means  that  a  prism  separates  the  rays  of  light  in  the 
order  of  their  wave-lengths. 


236 


NATURAL    PHILOSOPHY. 


In  order  to  see  these  colors  to  the  best  advantage,  it 
is  better  to  employ  a  slot  through  which  the  sunlight  is 
directed  (Fig.  125).  It  may  be  an  inch  long  and  the  six- 
teenth of  an  inch  broad.  A  slit  cut  in  paper  will  answer 
if  a  metallic  adjustable  apparatus  is  not  at  hand.  In 
the  path  of  this  narrow  beam  when  it  enters  the  room, 
place  a  lens  of  ten  or  twelve  inches'  focus  and  move  it 
in  the  beam  until  a  sharply  defined  and  enlarged  image 
of  the  slit  is  seen  on  the  opposite  wall ;  then  place  the 


FIG.  125. 

prism  in  front  of  the  lens  and  near  it.  The  beam  will 
be  bent  to  the  side  of  the  room  and  a  spectrum  will 
appear,  the  length  of  which  will  depend  upon  the  dis- 
tance to  the  wall  or  screen  and  also  upon  the  kind  of 
prism  used.  A  dense  glass  prism  should  give  at  20 
feet  a  spectrum  about  3  feet  long.  A  bottle  prism  of 
bisulphide  of  carbon  will  give  one  4  feet  long.  By 
turning  the  prism  this  way  or  that,  a  position  will  be 
found  where  the  deflection  of  the  whole  is  least,  and  if 
the  prism  be  turned  either  way  from  this,  the  spectrum 
will  move  aAvay  in  the  same  direction.  This  deflection 
is  called  the  angle  of  least  deviation.  Prisms  of  crown 
glass,  of  quartz,  of  salt,  or  water,  when  tested  in  this 


ETHKI:   WAVES.  237 

way  show  that  for  each  there  is  an  angle  of  least  devia- 
tion different  from  any  of  the  others. 

Spectrum  Analysis.  —  The  colored  fires  seen  in  fire- 
.  works  are  produced  by  igniting  some  of  the  salts  of  the 
metals.  If  a  loop  of  platinum  wire  be  dipped  into  salt 
water,  and  then  be  held  in  the  flame  of  a  Bunsen  burner 
or  an  alcohol  flame,  the  flame  will  be  colored  bright 
yellow.  If  the  wire  be  dipped  into  a  solution  of  lithium 
chloride,  it  will  color  the  flame  red ;  potassium  chloride 


will  color  it  purple ;  copper,  a  greenish  blue.  These 
different  colors  signify  that  different  wave-lengths  are 
produced  by  the  vibrating  molecules.  If  such  light  be 
sent  through  a  prism,  it  is  found  to  give,  not  a  spectrum 
like  the  sunlight,  but  a  spectrum  of  its  own,  peculiar  to 
each  element,  and  like  no  oth&r.  The  better  to  observe 
these  an  instrument  has  been  devised  called  a  spectro- 
scope (Fig.  126),  consisting  of  a  tube  A  carrying  a  slot, 
through  which  the  light  goes  to  the  triangular  prism  of 
flint  glass.  This  disperses  the  waves  in  the  order  of 
their  wave-lengths,  and  they  pass  on  into  a  short  tele- 
scope B  for  conveniently  examining  the  spectrum  pro- 
duced. Thus  it  is  found  that  sodium  gives  one  yellow 


238 


NATURAL    PHILOSOPHY. 


image  of  the  slot,  and  it  is  called  a  yellow  line.  Lithium 
gives  a  red  line.  Copper  gives  blue  and  green  lines. 
The  bright  lines  produced  in  this  way  are  called  the 
spectra  of  the  elements.  So  it  is  possible  to  make  a 
chart  of  the  spectra  of  all  the  elements.  The  wave- 
length of  the  yellow  light  given  out  by  sodium  is 
about  the  forty-four  thousandth  of  an  inch;  that  of 
the  red  light  of  lithium,  the  forty-two  thousandth 
of  an  inch.  Most  of  the  chemical  elements  give  out 
rays  of  many  different,  but  of  definite,  wave-lengths; 
but  whatever  number  they  give,  the  wave-length  is 
uniform.  The  yellow  light  of  sodium  and  the  red 
light  of  lithium  have  always  the  same  positions  in  the 
spectrum.  This  means  that  each  kind  of  a  molecule 
produces  waves  of  a  given  length,  and  a  mixture  of 
different  elements  will  not  prevent  them  from  doing  so 
when  in  a  flame.  Each  one  will  give  its  own  spectrum 
independent  of  the  rest. 

If  the  light  from  an  electric  arc  be  examined  in 
the  same  way  as  the  sunlight,  by  sending  it  through 


FIG.  127. 


a  slot  in  a  lantern  and  then  through  a  prism  (Fig.  127), 
it  is  found  to  give  a  spectrum  like  the  sun,  all  the 
colors  in  the  same  order.  It  gives  a  complete  spec- 


ETHER    WAVES.  239 

trum  instead  of  a  partial  one,  as  is  given  by  the  sub- 
stances just  described.  This  is  true  for  all  kinds  of 
solid  bodies  which  are  made  hot  enough  to  shine  and 
give  out  light  waves  ;  also  for  glowing  liquids  like 
melted  iron  or  other  metals. 

The  explanation  of  this  great  difference  between  the 
spectra  of  solids  and  liquids  and  of  gases  requires  the 
reconsideration  of  the  molecular  conditions  in  these 
different  states  of  matter.  Suppose  a  large  number  of 
bells  were  shaken  together  in  a  basket,  there  would  be 
a  great  jingle  of  sounds,  but  no  one  of  the  bells  could 
give  out  its  own  sound  because  its  vibrations  would  be 
interfered  with  by  its  touching  neighbors.  In  solids 
the  molecules  cohere  even  at  a  high  temperature,  and 
being  practically  in  contact  with  each  other,  their  vibra- 
tory motions  continually  interfere  with  each  other.  At 
a  high  temperature  they  are  all  vibrating  at  rates  which 
give  out  light  waves,  but  no  one  of  them  has  time  to 
complete  a  vibration  before  it  is  interfered  with  by  the 
bumpings  of  the  adjacent  molecules  which  compel  it 
to  vibrate  irregularly,  in  all  periods,  and  thus  produce 
irregular  wave-lengths,  some  long  and  some  short, 
which  follow  each  other.  When  rays  made  up  of  such 
irregular  waves  come  to  a  prism  which  separates  the 
waves  in  the  order  of  their  lengths,  they  are  spread  out 
into  the  spectrum,  and  we  see  a  continuous  one,  made 
up  of  the  ether  waves  of  all  lengths  which  can  affect 
the  eye,  and  many  more  both  longer  and  shorter  that 
cannot  affect  it.  Such  solid  bodies  must  produce  waves 
of  all  lengths  :  whether  they  are  composed  of  one  element 
or  another  does  not  matter.  The  result  is  due  to  their 


240  NATURAL  PHILOSOPHY. 

compactness.  In  liquids,  too,  the  same  interference 
takes  place  among  the  vibrating  molecules  when  they 
are  heated  to  incandescence.  They  therefore  give  a 
continuous  and  complete  spectrum  like  solids. 

With  gases  it  is  very  different.  It  has  been  pointed 
out  on  page  13  that  in  the  air  the  molecules  have  an 
average  free  path  between  the  impacts  something  like 
two  hundred  times  their  own  diameter.  They  have, 
therefore,  time  to  vibrate  at  their  own  periodic  rate  ivith- 
out  'any  interference  a  great  many  times  a  second.  Thus, 
if  a  molecule  of  hydrogen  when  vibrating  gives  out  red 
light  having  a  wave-length  of  one  forty-thousandth  of 
an  inch,  it  shows  that  it  is  vibrating  as  many  times  a 
second  as  one  forty-thousandth  of  an  inch  is  contained 
in  186,000  milos.  This  is 

186,000  X  5280  X  12 

^ =  450  millions  of  millions. 


40,000 

It  collides  with  others  nearly  20,000  millions  of  times 
per  second,  yet  between  any  two  impacts  it  has  time  to 
make 

450  millions  of  millions       nn  -Arv     ., 

—  =  22,500  vibrations 
20,000  millions 

without  being  interfered  with  for  every  one  that  is  in 
any  way  hindered,  so  the  waves  are  nearly  all  of  a 
uniform  length.  The  prism  refracts  them  all  alike,  and 
thus  produces  a  spectrum  characteristic  of  the  substance 
and  also  of  its  condition  as  a  gas.  An  incandescent 
solid  gives  a  continuous  spectrum,  and  incandescent 
gas  gives  a  discontinuous  bright  line  spectrum.  In 


ETHER    WAVES.  241 

the  experiments  described  with  the  solutions  of  salts 
giving  colored  flames,  it  is  to  be  remembered  that  in 
the  flame  the  solutions  are  at  once  converted  to  gas, 
and  the  molecules  have  the  free  path  needed  for  giving 
their  proper  spectra. 

If  the  tip  of  the  lower  carbon  of  an  arc  lamp  have 
a  cavity  made  in  it  for  holding  in  turn  small  bite  of 
different  metals  such  as  copper,  zinc,  and  silver,  when 
the  upper  carbon  touches  it  the  metal  is  not  only  fused 
but  is  vaporized  ;  its  high  temperature  causes  it  to  give 
out  light  with  its  characteristic  wave-length  and  color. 
And  these  may  be  thrown  upon  the  screen  with  the 
apparatus  shown  in  Fig.  127. 

Absorption  Power  of  Gases.  —  Produce  a  good 
continuous  spectrum  with  either  sunlight  or  an  arc 
light  as  described  on  page  235.  Then  with  a  gas  flame 
vaporize  a  lump  of  sodium  as  large  as  a  pea  in  an  iron 
spoon,  and  hold  it  in  the  path  of  the  rays  between  the 
slot  and  the  prism.  The  spectrum  upon  the  wall  will 
now  be  seen  to  have  a  well-defined  and  very  black  line 
across  the  yellow  part,  due  to  the  fact  that  the  gaseous 
molecules  of  the  elements  are  able  to  absorb  and  stop 
such  waves  as  they  are  themselves  able  to  produce. 
These  are  therefore  abstracted  from  the  beam,  while  the 
remainder  go  on  and  form  the  rest  of  the  spectrum. 
The  black  line  thus  produced  is  called  an  absorption 
line,  and  is  as  much  characteristic  of  the  element  sodium 
as  is  the  bright  yellow  light  which  itself  can  produce. 
It  indicates  more  than  this,  for  it  shows  the  existence  of 
a  source  of  light  behind  it  which  is  either  solid  or  liquid, 


242  NATURAL   PHILOSOPHY. 

and  that  itself  is  in  the  gaseous  form,  else  it  could  not 
absorb  the  particular  rays  it  does. 

.  By  making  the  slot  of  the  spectroscope  quite  narrow 
and  examining  sunlight  with  it,  the  spectrum  is  seen  to 
be  crossed  by  a  large  number  of  fine  black  lines  parallel 
to  each  other.  They  may  be  shown  on  the  wall  by 
making  the  slot  in  the  apparatus  (Fig.  125)  narrow, 
and  nicely  focusing  it  before  placing  the  prism  in  its 
path.  One  may  observe  a  line  in  the  yellow,  several 
in  the  green  and  in  the  blue,  and  some  broad  ones  near 
the  limit  at  the  violet  end  of  the  spectrum  ;  and  with 
a  lens  having  a  focal  length  of  four  or  five  feet,  some 
hundreds  may  be  seen.  These  black  lines  in  the  solar 
spectrum  are  known  as  Fr-aunhofer  lines  —  named  after 
the  one  who  first  studied  and  made  a  chart  of  them. 

Their  origin  is  the  same  as  the  black  sodium  line 
already  described  as  due  to  absorption  in  a  gaseous 
medium.  The  body  of  the  sun  that  gives  out  most  of 
the  light  appeal's  to  be  an  incandescent  solid  or  liquid, 
and  gives  out  light  of  all  wave-lengths.  Its  temperature 
is  so  high  that  all  substances  at  its  surface  have  more 
or  less  a  gaseous  form ;  that  is,  the  atmosphere  of  the 
sun  is  made  up  of  the  highly  heated  gases  of  the  sub- 
stances that  compose  the  body  of  the  sun.  The  light 
from  the  latter  has  to  travel  through  a  great  many  miles 
of  this  atmosphere,  and  in  it  absorption  goes  on,  each 
element  stopping  those  waves  which  belong  to  its  period 
of  vibration.  When  the  beam  of  light  reaches  the  earth 
it  has  lost  some  of  the  constituents  it  started  with. 
The  Fraunhofer  lines  indicate  which  ones  have  been 
lost,  and  measuring  the  corresponding  wave-lengths 


ETHER    WAVES.  243 

enables  one  to  discover  the  elements  which  are  present 
in  the  atmosphere  of  the  sun.  Nearly  every  element 
we  are  acquainted  with  on  the  earth  has  been  identified 
by  the  lines  seen  in  the  solar  spectrum,  some  elements 
giving  but  a  few  lines,  others,  such  as  iron,  giving 
several  hundred. 

The  spectra  given  by  the  moon  and  planets  show 
the  same  lines  as  those  given  by  the  sun  ;  for  the 
light  from  them  is  only  sunlight  reflected  from  solid 
bodies,  which  do  not  change  the  character  of  the 
light,  only  its  direction.  The  spectra  of  stare  show 
similar  constitution  and  condition  to  the  sun,  but 
differ  in  the  relative  amounts  of  the  different  elements 
present. 

Comets  give  gaseous  spectra,  much  hydrocarbon 
being  present ;  and  many  cloudy  patches  in  the  sky, 
called  nebulae,  seem  to  be  altogether  gaseous  with 
hydrogen  in  abundance.  In  the  long  reaches  of  space 
between  the  stare  and  the  earth  there  are  stray  mole- 
cules of  many  kinds  which  by  their  absorptive  action 
show  their  presence  in  small  quantities.  Benzine  and 
other  alcohol  derivatives  are  particularly  noticeable. 
Thus  a  beam  of  light  can  inform  us  of  the  kind  and 
quality  of  matter  from  which  it  originated,  whether  it 
was  solid  or  gaseous,  and  the  kind  and  condition  of  the 
matter  through  which  it  has  passed.  The  elements  that 
are  present  in  the  sun  and  its  condition  are  as  definitely 
known  as  it  would  be  if  it  were  no  more  than  a  thousand 
miles  away  instead  of  being  so  many  millions,  for  ether 
waves  do  not  change  their  character  nor  their  wave- 
length by  traveling  in  free  space. 


244 


NATURAL    PHILOSOPHY. 


Invisible  Waves.  —  We  know  that  sunshine  warms 
the  earth,  and  the  hand  feels  the  warmth  of  the  direct 
rays.  When  a  spectrum  is  formed  of  the  sunlight,  the 
rays  are  spread  out  into  a  band,  as  already  described 
on  page  235,  and  if  one  reflects  upon  the  fact  that 
the  waves  represent  the  heat  energy  of  the  sun,  lie 
might  expect  to  find  this  energy  distributed  through 
the  spectrum  ;  but  if  the  hand  be  held  in  it,  it  does  not 
appear  to  be  warm  in  any  part.  This  is  because  the 
amount  of  light  used  to  produce  the  spectrum  is  small, 


Y 


FIG.  128. 


and  it  is  so  much  diffused  that  the  heat  is  not  great 
enough  to  be  felt.  If  more  delicate  means  are  em- 
ployed to  test  it,  the  heating  effect  is  found  in  every 
part  of  it.  For  this  purpose  a  delicate  thermopile 
may  be  taken.  When  its  face  is  heated  it  produces  a 
current  of  electricity,  and  if  the  wires  are  connected 
to  a  delicate  galvanometer,  its  needle  is  moved  and 
indicates  the  difference  in  temperature.  Let  the  face 
of  such  a  thermopile  (Fig.  128)  be  moved  through 
the  spectrum  not  very  far  from  the  prism,  the  gal- 
vanometer needle  shows  great  difference  in  different 
parts  of  the  spectrum.  It  indicates  but  little  at  the 


ETHER    WAVES. 


245 


blue  end  b,  but  shows  more  and  more  as  it  is  moved 
through  the  green  and  yellow,  and  is  very  much  greater 
at  a  in  the  red.  If  it  be  moved  beyond  the  red  towards 
d,  where  there  is  no  light  of  any  color  to  be  seen,  the 
needle  shows  still  more  heat  than  elsewhere,  and  proves 
that  there  are  waves  beyond  the  red  that  have  more 
energy  than  any  in  the  visible 
spectrum,  and  that  they,  too,  are 
refracted  like  the  waves  that  can 
be  seen. 

A  bolometer  is  much  more  sensi- 
tive than  a  thermopile.  It  con- 
sists of  a  thin  filament  of  carbon  f  (Fig.  129),  which 
makes  a  part  of  an  electric  circuit  with  a  battery  B 
and  a  galvanometer  0.  The  resistance  of  the  circuit 
is  changed  by  different  temperatures  of  the  filament, 
and  the  needle  of  the  galvanometer  indicates  the 
changes.  When  this  filament  is  moved  through  the 


FIG.  129. 


/      GAS       X 

*RC  ;'--_      - 


47        54       03        70       78       «5        U3       101      1UU     ll'i 
FIG.  130. 


spectrum,  the  presence  of  the  FYaunhofer  lines  is  shown 
by  the  falling  of  the  temperature  in  the  filament.  With 
this  instrument  the  distribution  of  energy  in  the  whole 
spectrum  has  been  charted  (Fig.  130),  and  it  shows  a 


246  NATURAL   PHILOSOPHY. 

curious  lack  of  uniformity.  In  this  diagram  the  visible 
spectrum  is  that  between  0  and  the  vertical  dotted  line. 
All  to  the  right  of  that  line  is  below  the  red  and  there- 
fore of  greater  wave-length  ;  this  part  extends  to  several 
times  the  length  of  the  visible  part,  with  a  number  of 
places  where  there  are  gaps,  showing  the  lack  of  pro- 
portional parts  of  certain  wave-lengths. 

The  line  marked  arc  shows  a  different  but  more  uni- 
form distribution  of  energy,  the  greatest  amount  being 
far  below  the  red  end.  The  curve  for  gas  has  its  maxi- 
mum still  further  away  and  rises  higher.  The  relative 
amount  of  energy  in  the  visible  part  is  greatest  in 
sunlight,  and  is  at  its  maximum  in  the  brightest  part 
of  the  spectrum,  the  yellow.  In  the  experiment  tried 
as  above,  the  greatest  effect  will  be  found  below  the 
red;  but  that  is  occasioned  by  the  fact  that  the  glass 
prism"  absorbs  a  large  amount  of  the  energy  of  those 
visible  waves  and  becomes  heated. 


PHOTOGRAPHY. 

Beyond  the  violet  there  are  still  shorter  waves,  with 
but  a  small  amount  of  energy,  yet  able  to  affect  mole- 
cules of  some  kinds  so  as  to  produce  chemical  decom- 
position. If  a  spectrum  be  directed  upon  an  ordinary 
photographic  plate,  the  plate  will  not  be  affected  by  the 
red  and  yellow  rays  ;  by  the  green  it  will  be  affected 
slightly,  but  increasingly  towards  the  blue  and  violet, 
and  beyond  these  decreasingly  to  some  distance,  thus 
showing  that  there  are  waves  too  short  to  be  seen,  and 
with  too  little  energy  to  affect  coarser  apparatus,  yet 


ETHEK    WAVES.  247 

enough  to  affect  molecules  and  decompose  them,  for 
that  is  what  happens  in  photography.  The  material  in 
common  use  for  making  a  surface  sensitive  to  light  is 
the  bromide  or  the  iodide  of  silver — substances  that  are 
not  very  stable  compounds  ;  the  light  of  these  short 
wave-lengths  dislocates  their  atoms.  The  solution  into 
which  the  plate  is  put  after  exposure  washes  out  the 
bromine  or  the  iodine  and  leaves  the  silver  in  a  deposit, 
which  is  thicker  or  thinner  as  the  action  of  the  light  has 
been  greater  or  less.  By  mixing  with  the  silver  solu- 
tion such  substances  as  the  anilines,  the  whole  is  affected 
by  longer  waves,  and  in  this  way  the  whole  spectrum 
has  been  photographed  below  the  red  end  as  well  as 
all  the  visible  spectrum.  Photographic  action  is  the 
changing  of  molecular  structure  by  means  of  ether 
waves,  and  different  kinds  of  molecules  are  most  affected 
by  different  wave-lengths.  It  happens  that  silver  salts 
are  more  sensitive  to  the  waves  called  blue,  but  what 
are  called  Slue  prints  are  made  with  salts  of  iron. 

In  nature  the  photographic  action  of  sunlight  is  to 
be  seen  in  every  direction.  The  darkening  of  shingles 
and  clapboards  on  houses,  the  fading  of  the  colors  of 
fabrics  and  of  paints,  the  tanning  of  the  skin  exposed  to 
the  light,  the  coloring  of  flowers  and  of  fruit,  which 
will  not  take  place  if  kept  in  darkness,  are  all  the 
result  of  molecular  changes  brought  about  by  the 
action  of  ether  waves  ;  not  any  particular  kind  of 
waves  for  all,  but  each  substance  is  more  affected  by 
some  kinds  than  by  others. 

A  thick  paper  star  or  other  design  if  pinned  to  the 
freshly  planed  surface  of  pine  or  white  wood,  or  pasted 


248  NATURAL    PHILOSOPHY. 

to  the  side  of  a  green  apple  and  left,  will  have  its  out- 
line photographed  after  exposure  to  sunlight. 

I.  Electric  Photography.  —  In  ordinary  photography 
the  sensitized  surface  is  acted  upon  by  ordinary  light 
waves  such  as  can  affect  the  eye,  but  waves  originated  by 
electric  action  and  much  longer  are  competent  to  do  the 
same  thing  in  the  dark.     Paste  a  piece  of  tin  foil,  as 
large  as  the  hand,  upon  a  sheet  of  glass  twice  as  large, 
and  connect  the  foil  by  a  wire  to  one  of  the  discharging 
rods  of  a  Holtz  or  Wimshurst  electric  machine.  Another 
glass  prepared  in  similar  way  and  connected  to  the  other 
rod  of  the  machine  may  be  laid  upon  the  first,  the  two 
glass  sides  together.    When  the  machine  is  worked  and 
sparks  pass  between  the  knobs,  electric  waves  will  pass 
between  the  sheets  of  tin  foil  through  the  glass,  and  if 
a  sensitive  photographic  plate  in  its  holder  be  placed 
between  the  glass  plates,  it  will  be  acted  upon  as  if  in 
the  light.     A  coin  placed  upon  the  holder  will  have  its 
image  impressed  upon  the  sensitized  plate,  and  it  may 
be  developed  in  the  common  way.     Such  pictures  are 
called  electrographs. 

II.  X-Ray  Pictures.  —  When    a  highly  exhausted 
Crookes'  tube    is  lighted    up  by  electrical   discharges 
from  a  glass-plate  machine  or  induction  coil,  the  char- 
acter of  the  discharge  is  seen  to  be  unlike  at  the  two 
inner  terminals.     The  wire  terminal,  which  leads  the 
electricity  into  the  tube,  is  called  the  anode,  and  the 
one  leading  out  of  it,  the  cathode;  electrical  discharges 
from  the  latter  produce  upon  the  inner  surface  of  the 


KTMKK     \VAVKS. 


249 


glass  the  greenish  phosphorescence,  which  can  be  seen, 
and  upon  the  outer  surface  invisible  waves  which  pass 
freely  through  wood,  the  fleshy  part  of  the  hand,  or  other 
parts  of  the  body,  and  still  produce  phosphorescence. 


FIG.  131. 

By  using  a  screen  coated  with  phosphorescent  material, 
such  as  the  tungstate  of  calcium  or  platinocyanide  of 
barium,  inclosed  in  a  dark  box  (Fig.  131),  one  may  see 
in  these  radiations  from  the  tube  the  coin  in  a  closed 
pocketbook,  the  shadows  of  the  bones  in  the  hand, 
and  pieces  of  metal  imbedded  in  the  flesh.  The  same 
radiations  act  upon  a  photographic  plate  inclosed  in  its 


250  NATURAL   PHILOSOPHY. 

holder  if  held  near  the  tube.  As  these  radiations  are 
not  reflected,  refracted,  nor  polarized  like  ordinary  rays 
of  light  such  as  affect  the  eye,  they  have  been  called 
X-rays,  to  indicate  an  unfamiliar  form  of  radiant  energy. 

MECHANICAL    EFFECTS    OF    ETHER    WAVES. 

The  Radiometer.  —  It  has  been  stated  that  when- 
ever ether  waves  of  any  length  fall  upon  matter  of  any 
kind,  some  of  it  is  reflected,  else  the  body  could  not  be 
seen,  and  some  of  it  is  absorbed  by  the  body.  Such  as 
is  absorbed  is  at  once  transformed  into  heat  and  raises 
the  temperature  of  the  substance.  A  surface  painted 
black  absorbs  nearly  all  the  radiant  energy  that  falls 
upon  it,  and  so  may  become  hot  in  sunlight.  A  body 
with  a  surface  hotter  than  the  air  adjacent  to  it  is  con- 
tinually heating  the  air.  The  molecules  of  air  that 
strike  upon  the  body  are  beaten  back  with  more  energy 
than  they  had  before  striking,  and  their  rebound  reacts 
upon  the  surface  producing  a  pressure  upon  it.  This  in- 
creased pressure  is  made  apparent  by  the  device  called 
the  radiometer.  It  consists  of  a  small  mill  made  with 
disks  of  mica  abed  (Fig.  132)  blackened  on  one  side 
and  fastened  to  four  arms  mounted  so  as  to  spin  upon 
a  needle  point,  the  whole  inclosed  in  a  glass  bulb  from 
which  a  large  part  of  the  air  has  been  drawn.  When 
radiant  energy  falls  on  the  blackened  surface  of  a,  the 
surface  is  heated  more  than  when  an  equal  amount  falls 
on  an  equal  surface  of  mica  c  not  so  blackened.  The 
molecules  of  air  will  bound  away  with  greater  velocity 
and,  therefore,  with  more  energy  than  they  had  when 


ETHER    WAVES. 


251 


they  struck  that  surface,  and  will  produce  a  pressure 
tending  to  move  the  disk  backwards  in  the  direction  of 
the  arrow.  If  the  mill  wheel  is  delicately  poised  and 
light  enough,  it  will  turn  until  the  disk  on  b  is  in  the 
position  in  which  a  is  represented  to  be,  and  so  keep  up 
a  continuous  rotation.  If  the  air  be  of  common  density 
instead  of  being  reduced,  the  free  path  would  be  a  short 
one,  and  the  quickened  motion  of  the  molecule  would 
be  handed  over  to  the 
one  next  it,  and  so  con- 
ducted away  even  to 
the  other  side  of  the 
disk  before  the  disk 
would  have  time  to 
move.  With  less  den- 
sity and  longer  free 
paths,  this  distribution 
of  gaseous  pressure  can- 
not go  on  so  fast,  and  the  disks  move.  It  is  not 
the  impact  of  ether  waves  upon  the  disks  that  pro- 
duces the  pressure ;  the  radiant  energy  is  transformed 
into  heat  —  molecular  vibrations — and  this  into  the 
mechanical  pressure  of  free-moving  gaseous  molecules. 
A  delicate  radiometer  will  show  by  the  rate  of  its 
rotation  the  difference  in  the  distribution  of  the  energy 
in  the  spectrum  better  than  the  thermopile  and  galva- 
nometer show  it,  as  represented  in  Fig.  128. 

Double  Kefnu-tioii.  —  When  a  clear  crystal  of  Ice- 
land sp;ii-  is  laid  on  a  printed  page,  every  letter  seen 
through  it  appears  double,  and  the  distance  apart  of  the 


252 


NATURAL   PHILOSOPHY. 


images  depends  upon  the  thickness  of  the  crystal.  If 
the  crystal  be  twisted  round,  one  of  these  appears  to 
revolve  about  the  other.  This  may  be  seen  to  great 
advantage  by  directing  a  small  beam  of  sunlight  through 


the  crystal,  and  then  with  a  lens  projecting  the  two 
images  that  will  be  formed  of  the  hole,  as  in  the  dia- 
gram. By  rotating  the  spar  on  the  beam  as  an  axis, 
one  of  these  images  will  go  about  the  other.  This 
means  that  the  light  that  produces  the  second  image 
always  goes  through  the  spar  in  a  certain  direction  that 
depends  upon  the  molecular  arrangement  in  the  spar 
itself.  On  examining  the  spar  it  will  be  noticed  that  it 

has  acute  and  obtuse 
angles,  and  each  face 
is  a  rhomb  (Fig.  135). 
When  the  light  falls 
upon  one  of  these 
faces,  a  part  of  it  goes 

through  nearly  in  a  straight  path  ab;  the  other  is 
refracted  toivards  the  obtuse  angle  and  emerges  at  a 
distance  from  the  first,  and  then  goes  on  parallel  with 
it  as  shown  in  Fig.  134.  The  ray  ac  that  is  most 
refracted  is  called  the  ordinary  ray,  for  it  follows 


ETHER    WAVES.  253 

the  common  law  of  refraction  the  same  as  for  glass. 
The  other  ray  ab  does  not  follow  that  law,  and  is  for 
that  reason  called  the  extraordinary  ray.  This  phe- 
nomenon is  called  double  refraction.  If  common  white 
light  be  used  for  these  experiments,  both  these  images 
appear  alike  in  brightness,  but  they  both  show  another 
property  not  possessed  by  common  white  light.  Let  a 
second  piece  of  spar  similar  to  the  first  be  placed  be- 
tween it  and  the  lens  in  Fig.  133,  so  the  light  of  both 
beams  will  fall  upon  it,  each  of  these  two  beams  will 
again  be  divided  ;  now  if  one  of  the  spare  be  rotated  as 
at  first,  two  of  the  beams  will  rotate  about  the  others, 
but  at  certain  positions  one  pair  of  them  will  disappear, 
and  at  right  angles  to  this  the  other  pair  will  disappear, 
while  the  former  ones  will  be  bright,  showing  that 
whether  the  light  gets  through  the  second  prism 
depends  upon  its  position. 

Polarized  Light.  —  Let  a  piece  of  glass,  the  size  of 
the  glass  in  the  porte-lumiere  be  painted  black  on  one 
side  so  as  to  absorb  all  the  light  that  goes  through  the 
glass  to  it ;  fix  it  over  the  re- 
flector of  the  porte-lumiere  so  as 
to  be  used  as  a  reflector  in  its 
stead.  The  light  reflected  from 
this  blackened  glass  will  be  seen 
to  be  much  less  than  that  from 
the  silvered  surface  of  the  com- 
mon mirror.  Direct  a  small  beam  of  this  light  through 
the  spar  as  before,  and  rotate  the  spar.  When 
the  shorter  axis  A  B  of  the  face  of  the  spar  is  parallel 


254  NATURAL   PHILOSOPHY. 

with  the  inclination  of  the  blackened  glass  reflector,  the 
light  will  go  through  it ;  when  the  spar  has  been  turned 
through  90°  and  C  D  is  parallel  with  the  inclined  mirror, 
the  light  will  be  quite  shut  out,  as  was  the  case  in  the 

AA/WW 

FIG.  136. 

use  of  the  second  spar  in  the  former  experiment.  This 
phenomenon  may  be  understood  by  bearing  in  mind  that 
light  consists  of  wave  motions.  A  model  of  such  waves 
may  be  made  of  wire  bent  thus.  If  one  looks  along 
such  a  model  in  the  direction  of  its  length,  he  will 
see  only  a  short  straight  line.  All  the  waves  will 
be  in  one  plane,  and  of  course  could  go  through  a 
structure  as  between  the  fingers,  if  it  were  moved  in 
the  plane  of  the  fingers.  Turned  at  right  angles  to  the 

fingers,  it  would  not 
pass  through.  A  beam 
of  light  in  which  all 
the  waves  are  in  the 
same  or  parallel  planes 
is  called  a  plane  polar- 
ized beam,  and  any- 
thing that  causes  the 
waves  to  vibrate  in  this 

FIG.  137.  •          11-  j  7 

way  is  called  a  polar- 
izer. Such  light  as  is  reflected  from  this  front  surface  of 
the  blackened  glass  consists  of  waves  which  are  vibratiiuj 
in  planes  parallel  with  its  surface  as  ab  (Fig.  137).  The 
light  which  is  vibrating  in  a  plane  perpendicular  to 


ETHER    WAVES.  255 

the  surface  c  goes  through  the  glass  and  may  be  ab- 
sorbed by  the  black  back.1 

Hence  the  reflected  light  consists  of  light  waves 
that  are  vibrating  in  parallel  planes  and  is,  therefore, 
plane  polarized.  The  spar  permits  light  to  go  through 
it  in  only  two  planes,  ab  and  cd  (Fig.  134).  When, 
therefore,  the  light  reflected  from  the  glass  comes  to 
the  spar,  whether  it  gets  through  it  or  not  depends 
upon  whether  one  or  the  other  of 
the  spar's  planes  coincides  with  the 
plane  of  the  polarized  light.  A 
thin  section  of  a  piece  of  tourma- 
line (Fig.  138)  possesses  similar 
qualities  —  permitting  only  such 

,  .,  JVIG.  138. 

rays  to   go   through  it  as  are   vib- 
rating in  planes  parallel  with  its  length.     It  is,  there- 
fore,  a  polarizer,  and  two  such  pieces  crossed  upon 
each  other  stop  all  light,  though  apparently  both  are 
transparent. 

The  Nicol's  Prism.  —  If  a  long  piece  of  Iceland  spar 
be  cut  in  two  in  the  line  ab  (Fig.  139),  its  short  axis, 

and  then  cemented 
together  again  in 
the  same  position, 
the  extraordinary 
ray  c  dgoes  through 
without  trouble, 
while  the  ordinary  ray  which  meets  the  cut  surface  at  a 

1  Some  scientists  consider  the  plane  of  polarization  to  be  at  right  angles  to  the 

plat f  vibration.    In  this  book  the  plane  of  polarization  is  considered  the  same 

:isthe  plane  of  vibration. 


256 


NATURAL   PHILOSOPHY. 


smaller  angle  is  totally  reflected  and  goes  out  on  the 
side  near  a.  This  leaves  the  beam  at  d  composed  of 
rays  polarized  in  the  plane  of  the  shorter  axis  of  the 
face  AB  (Fig.  135).  This  is  called  a  NicoVs  prism,  and 
is  of  great  service  in  the  study  of  polarized  light.  With 
this  one  may  test  the  character  of  the  light  reflected 
from  any  surface  or  from  any  source.  Reflected  light 
from  most  surfaces,  as  from  the  floor,  table,  walls,  or 
the  sky,  is  thus  discovered  to  be  more  or  less  polarized, 
for  by  rotating  the  prism  the  light  appears  to  be  more 


FIG.  140. 


or  less  bright  according  to  the  angle  through  which  the 
prism  is  turned.  When  used  in  this  way  to  discover 
the  existence  of  polarized  light  and  its  plane,  it  is 
called  an  analyzer.  Let  a  large  beam  of  plane  polarized 
light  be  directed  through  the  lens  so  as  to  give  a  disk  of 
light  upon  the  screen  (Fig.  140).  If  the  Nicol's  prism  be 
put  in  the  focus  at  f,  so  that  all  the  light  goes  through 
it,  it  may  be  rotated  so  that  all  the  light  will  be  stopped 
and  the  screen  be  dark.  Let  a  sheet  of  mica  be  placed 
at  a,  the  light  at  once  goes  through  the  prism;  on  the 
screen  it  appears  of  some  color  which  depends  upon  the 
thickness  of  the  mica.  If  this  be  of  different  thickness, 
each  part  will  have  a  different  tint ;  and  if  a  geomet- 


ETHER    WAVES.  257 

ric  diagram  be  cut  in  it  having  different  thicknesses, 
the  diagram  will  show  in  bright  colors.  Rotating  the 
mica  in  its  own  place  will  change  these  tints.  Other 
thin  crystals  will  show  similar  effects,  especially  sele- 
nite,  and  microscopic  crystals,  if  projected  in  the  ordi- 
nary way  as  described  on  page  118,  often  will  show  in 
this  light  very  beautiful  tints,  and  may  be  identified  in 
this  way. 

These  results  are  due  to  the  fact  that  such  crystals 
are  double  refracting  and  break  up  each  ray  into  two 
parts  having  different  directions ;  when  placed  in  polar- 
ized light  from  some  other  source,  interference  is  pro- 


c 
FIG.  141. 


duced  and  some  of  the  elements  of  white  light  are 
cancelled,  leaving  the  rest  of  the  constituents.  How 
this  can  be  may  be  understood  by  taking  two  wire 
models  of  waves  of  equal  length,  as  a  and  b.  If  one  of 
these  as  a  be  moved  along  b  until  the  crests  of  its 
waves  are  over  the  troughs  of  b,  the  two  will  represent 
the  conditions  when  they  will  necessarily  cancel  each 
other.  This  takes  place  when  one  is  half  a  wave-length 
behind  the  other.  The  waves  of  light  are  so  short  that 
only  a  thin  section  of  a  crystal  is  needed  to  effect  this. 
Glass  that  is  not  well  annealed  shows  colors  when 
examined  in  polarized  light,  for  the  molecules  are  in 
a  state  of  stress  within  it,  and  are  not  in  stable  posi- 
tions :  double  refraction  takes  place  in  such  places, 
and  the  directions  of  the  stress  are  shown  by  the 


258 


NATURAL   PHILOSOPHY. 


colors  ;  they  vary  with  the  form  of  the  glass.  An- 
nealed glass  which  shows  no  colors  will  show  them 
plainly  if  bent  or  twisted  or  compressed. 


Diff 

direct* 

SI 

raction.  —  If    light 
d  through  a  small 

I 

From  the 
liole  intf 

1 

^ 

porte-lumiere   be 
>  a  room  which  is 
otherwise     dark, 
the  beam  may  be 
traced    straight 
across  the  room  to 
the  wall  or  screen 
by  the  dust  in  the 
air,  but  the  orifice 
itself  may  be  seen 
from  every  part  of 

V 

FIG.  142. 

^ 

the  room,  which  shows  that  light  is  to  some  extent 

deflected  at  that  point.     If  the  first  orifice  be  a  round 

hole  a  quarter  of   an  inch  in  diameter,  and  another 

similar  hole  be  cut  in  a  sheet  of  paper  A  and  placed  in  the 

line  of  the  beam,  another  sheet  of  white  paper  B  placed 

a  few  inches  beyond  will  show  a  series  of  colored  circles 

upon   it,    the    inner 

one  bluish,  and  the 

others  following  the 

same  order  as  that  in 

the    solar  spectrum. 

This  phenomenon  is 

called  diffraction,  and 

it  shows   that  ether 

waves    like    other 

kinds  set  up  waves  Flo  ,43 


ETHER    WAVES. 


259 


in  a  lateral  direction.  Let  abc  represent  waves  of 
water  moving  in  the  direction  of  the  arrow.  When  a 
reaches  the  wall  W,  with  an  opening  in  it  so  a  portion 
of  the  waves  can  go  through,  that  portion  will  not  only 
continue  on  towards  d,  but  will  spread  out  to  e  and  f, 
and  so  will  each  succeeding  wave. 

If  fine  lines  are  ruled  upon  a  piece  of  glass,  five 
hundred  or  more  to  the  inch,  and  a  beam  of  sunlight 
be  sent  through  it,  very  beautiful  spectra  can  be  pro- 
duced, showing  the  Fraunhofer  lines.  This  is  called 
diffraction  grating.  The  finer  the  rulings  of  these 
lines,  the  longer  is  the  spectrum.  The  colors  are 
produced  by  interference.  Thus,  let  A  and  B  (Fig.  144) 
represent  the  clear  space  between  the  lines  through 
which  the  rays  to  C  and  D  can  go  straight  forward.  At 
A  the  defracted  waves  start  towards  D,  E,  and  F,  where 
they  meet  with  other  waves  from  B.  It  is  plain  that 

ray  AD  has  traveled  a 
greater  distance  at  D  than 
has  B  D,  and  AE  than  B  E. 
Whenever  this  difference 
in  the  path  of  the  rays 
amounts  to  half  a  wave- 
length, the  interference 
_  cancels  them,  but  A  D 
would  be  shorter  than 
AF,  and  would  represent 
a  shorter  wave.  The  colors  then  begin  with  the  short- 
est visible  waves  —  the  blue  — and  continue  through  the 
spectrum  in  the  wave-length  order.  These  phenomena 
may  be  made  very  bright  and  plain  by  employing  the 


C         D 
FIG.  144. 


260 


NATURAL    PHILOSOPHY. 


porte-lumiere  and  a  slot  A  (Fig.  145),  the  twentieth 
of  an  inch  broad,  like  that  used  in  the  spectroscope, 
and  a  common  lens  0  for  sharply  focusing  the  image 


s 

1A      s     ° 

A              1 

& 

screen  S,  and  the 
grating  placed 
at  the  principal 
focus  in  front  at 
L.      It    is    with 
spectra     pro- 
duced    in     this 
way,  with  grat- 

\J 

FIG.  145. 

ing  ruled  43,000  lines  to  the  inch,  that  our  knowl- 
edge of  the  sun  and  stars  has  been  greatly  extended. 
Such  gratings  are  able  to  produce  spectra  forty  feet 
long,  and  a  great  amount  of  detail  may  not  only  be 
seen,  but  photographed. 

The  Eye  and  Vision. — The  physical  structure  of  the 
eye  is  in  many  particulars  quite  like  the  photographic 
camera,  the  latter,  of  course,  being  simpler  in  structure. 


FIG.  146. 


The  camera  C  (Fig.  146)  consists  of  a  box  having  an 
adjustable  lens  in  front  for  producing  an  image  upon 
the  sensitive  surface  placed  at  the  back.  In  like 


ETHER    WAVES. 


261 


manner  the  eye  is  a  globular  chamber  (Fig.  147)  having 

an  adjustable  lens  in  front  for  producing  an  image  upon 

a  sensitive  surface  at  the  back.   In  order  to  allow  more  or 

less  light  to  pass  through  the  camera  lens,  strips  of  metal 

called  diaphragms,  having  holes  of  different  sizes   in 

them,  are  placed  in  front  of  the  lens.    In  the  eye,  to  effect 

the  same  thing,  a  muscle  called  the  iris  (Fig.  148,  i,  i)  is 

fixed  so  its  contractions  in  different  degrees  change  the 

size  of  the  pupil  of  the  eye, 

the  pupil  E  being  the  orifice 

in  this  muscle.     The  iris  is 

of    different    colors    in    dif- 

rent  individuals,  being  blue, 

gray,  brown,  or  black.      A 

ratehet  wheel  in  the  camera 

enables  one  to  focus  sharply 

images  upon  the  back.     In 

the  eye  the  lens  F  is  itself 

provided  with  muscles  at  its  edge,  which  by  contracting 

make  the  convexity  greater  or  less,  and,  so  change  the 

focus. 

In  the  camera  the  sensitive  surface  upon  which  the 
picture  is  made  is  changed  by  the  removal  of  the 
prepared  plate.  In  the  eye  the  surface  is  contin- 
ually renewed  by  the  physiological  process  called 
secretion.  In  the  camera  the  sensitive  substances  upon 
the  plate  is  a  preparation  of  a  salt  of  silver.  In 
the  eye  the  sensitive  substance  is  a  complex  chemical 
compound  called  purpurine,  secreted  by  the  retina  D, 
which  is  the  name  of  the  surface  at  the  back  of 
the  eye. 


262 


NATURAL    PHILOSOPHY. 


The  globular  chamber  of  the  eye  H  is  filled  with  a  thin 
jelly-like  liquid  called  the  vitreous  humor.  The  lens  is 
a  transparent  elastic  body  made  up  of  layers  somewhat 
like  an  onion  ;  its  change  of  form  can  be  produced  by 

the  conscious  effort  to  pro- 

-j^ /^f=2':  /  ,><^  ducc  distinct  vision,  which 
<tip  svtfT>?i^wrTmy"~  is  called  adjustment.  In  the 
lisal^tlLr/^  /\||&i--  normal  eye  the  focus  of  the 
lens  is  at  the  retina,  but  in 
some  individuals  the  curva- 
ture of  the  lens  is  too  great 
or  too  small,  and  distinct 
vision  is  impossible  without 
aids.  If  the  lens  is  too 
much  curved,  the  focus  is 
too  short,  and  a  concave 
glass  is  needed  to  lengthen 
it.  In  the  other  case  the 
focus  of  the  lens  is  beyond 
the  retina,  and  it  must  be 
shortened  by  proper  convex 
lens. 

A  cross-section  of  the  ret- 
ina (Fig.  149),  when  exam- 
ined with  a  microscope,  is 
seen  to  be  a  complicated 
structure  made  up  of  a  num- 
ber of  distinct  layers  of  cells, 
rods,  and  cones.  These  are 
connected  with  the  nerves  which  are  spread  throughout 
and  gathered  together  in  a  bundle  at  the  back  of  the 


A,  the  inner  layer  of  the  retina, 
next  to  the  vitreous  humor. 

B,  the  layer  of  rods  and  cones. 

C,  the  hlack  layer  which  stops  all 
rays  from  going  Iteyond.     The 
light  reaches  the  rods  and  cones 
after  it  has  traversed  all  the  cell 
layers  between  A  and  B. 


ETHER    WAVES.  263 

eye  0  (Fig.  148) ;  this  is  called  the  optic  nerve,  and  goes 
to  the  base  of  the  brain.  Its  function  is  to  transmit 
retinal  disturbances  to  that  seat  of  sensation  in  the 
brain  called  the  semorium,  where  they  are  interpreted, 
and  we  are  then  able  to  say  we  see. 

Phenomena  of  Vision.  —  The  image  formed  upon 
the  retina  is  inverted  for  the  same  reason  that  images 
formed  by  lenses  in  other  places  are  inverted.  How  it 
is  we  see  things  upright  has  not  yet  been  explained. 
The  range  of  ether  wave-lengths  capable  of  affecting 
the  jjgtina  is  relatively  small  when  compared  with  all 
the  waves  present  (Fig.  130),  but  the  amount  of  energy 
needed  to  produce  vision  is  almost  incredibly  small. 
The  energy  of  a  wave  depends  upon  its  amplitude  ; 
how  small  that  must  be  in  waves  that  come  from  stars 
millions  of  millions  of  miles  away !  Their  wave-length 
does  not  change,  but  their  energy  is  inversely  as  the 
square  of  the  distance  they  have  traveled.  The  eye  is 
more  sensitive  than  any  photographic  preparation  yet 
discovered. 

It  is  a  physical  disturbance  that  produces  the  sensa- 
tion of  light,  and  this  may  be  effected  in  a  number  of 
\\a\s  without  these  waves.  Thus,  with  the  eyes  shut, 
let  one  press  with  the  finger  upon  the  eye  and  a  circle 
of  light  can  plainly  be  seen.  A  sudden  bump  upon  the 
head  or  an  electric  discharge  through  the  body  produces 
a  flash,  and  this  shows  that  light  is  not  a  thing  outside 
the  eye,  but  produced  by  a  physiological  effect  in  the  eye. 

Persistence  of  Vision.  — When  a  firebrand  is  swung 
round  there  appears  to  be  a  trail  of  fire  the  length 


264  NATURAL    PHILOSOPHY. 

of  which  depends  upon  how  fast  the  brand  moves. 
If  it  be  swung  round  at  the  rate  of  about  ten  revo- 
lutions a  second,  the  trail  makes  a  complete  circle. 
This  shows  that  the  sensation  of  the  light  does  not  cease 
the  instant  the  source  is  removed,  but  lasts  about  the 
tenth  of  a  second  for  light  not  very  bright,  and  it  may 
last  much  longer  for  any  bright  light.  If  the  sun  be 
glanced  at,  one  may  see  the  image  of  the  sun  for  some 
seconds,  even  on  closing  the  eyes.  If  a  well-lighted 
window  be  steadily  looked  at  for  a  few  seconds,  and  the 
eyes  then  be  turned  to  a  dimly  lighted  wall,  the  window 
frame  may  be  plainly  seen.  This  implies  that  after 
action  the  retina  requires  a  short  time  to  replace  by 
secretion  the  used-up  material.  Until  that  be  done 
completely,  there  will  be  parts  of  the  retina  less  sensi- 
tive than  the  rest,  and  these  parts  will  give  a  visual 
image  less  bright  than  the  remainder. 

COLOR    SENSATION. 

Complementary  Colors.  — With  the  porte-lumiere 
and  apparatus  (p.  229),  project  a  disk  of  light  3  or  4  feet 
in  diameter  upon  the  screen.  Insert  a  piece  of  red 
glass  in  the  beam  so  as  to  make  the  disk  red.  Now 
look  steadily  at  the  middle  of  the  disk  for  five  seconds ; 
the  red  glass  may  then  be  removed  while  the  eyes  are 
still  looking  at  the  same  point  upon  the  screen.  The 
disk  will  now  look  decidedly  green.  If  green  glass  be 
substituted  for  the  red  and  the  experiment  tried  again, 
the  disk  will  appear  red.  Blue  glass  will  give  an  after 
effect  of  yellow,  and  yellow  will  give  one  of  blue.  If 


ETHER    WAVES.  265 

half  the  disk  be  colored  with  one  glass,  and  the  other 
half  with  some  other,  when  the  glass  is  removed  the 
two  halves  will  show  different  colors.  The  two  colors 
that  stand  related  to  each  other  in  this  way  are  comple- 
mentary colors.  This  shows  not  only  persistence  of 
vision  as  in  the  former  case,  but  also  that  a  portion  of 
the  retinal  sensitive  substance  may  be  affected  by  light 
of  certain  wave-lengths,  while  the  remainder  is  not 
affected,  and  is,  therefore,  fresh  for  use  when  white 
light  acts  upon  it.  Such  phenomena  have  led  to  the 
belief  that  the  photographic  material  of  the  eye  is  com- 
posed of  three  or  four  constituents,  one  of  them  sensi- 
tive to  red  waves,  another  to  the  green,  the  third  to 
blue,  and  possibly  one  to  degrees  of  black  and  white. 
If  red  rays  alone  act  upon  the  eye,  the  other  components 
will  not  be  affected.  When  the  red  material  is  used 
up  and  white  light  is  again  presented,  the  yellow, 
green,  and  blue  rays  give  together  a  sensation  of  green, 
for  yellow  light  and  blue  light  when  mixed  produce 
whiteness,  as  can  be  seen  by  combining  the  colors  of  the 
spectrum  with  a  mirror  so  that  one  color  can  lap  upon 
another  ;  this  leaves  the  green  as  the  complementary 
color  to  red.  In  general,  a  complementary  color  is  one 
which,  mixed  with  another,  will  produce  white  light.. 
From  such  phenomena  as  these,  it  appeal's  that  vision 
depends  upon  the  energy  acting  upon  the  physiological 
structure  of  the  eye,  what  we  call  light  being  such 
ether  waves,  set  up  by  vibrating  atoms,  as  can  affect 
the  sensitized  surface  of  the  retina.  Similar  waves  that 
are  longer  or  shorter  than  these  do  not  affect  our  eyes. 
It  is  probable  that  some  other  living  things,  such  as 


266  NATURAL  PHILOSOPHY. 

rats,  mice,  bats,  and  insects  of  various  kinds,  have  eyes 
sensitive  to  other  wave-lengths,  for  they  appear  to  see 
plainly  when  all  is  darkness  to  us.  If  our  eyes  were 
affected  by  waves  of  all  lengths,  there  would  be  no 
such  condition  as  darkness,  for  as  has  before  been 
pointed  out  (p.  206),  all  bodies  are  always  radiating 
waves  of  some  length.  Only  at  absolute  zero  could 
there  be  entire  absence  of  ether  waves. 

Phosphorescence.  —  Our  ordinary  sources  of  light, 
whether  the  sun  or  artificial,  like  fire  or  incandescence 
of  electric  lights,  are  produced  by  high  temperatures, 
the  sun  being  an  exceedingly  hot  body,  as  is  an  elec- 
tric arc.  When  an  ordinary  body  like  a  cannon  ball 
is  heated  it  begins  to  shine,  that  is,  gives  out  waves 
we  can  see,  at  about  1000°.  These  waves  are  about 
the  forty-thousandth  of  an  inch  long  and  produce  the 
sensation  of  redness.  As  the  ball  is  heated  hotter,  the 
waves  become  shorter  and  shorter  until  all  the  rays  we 
can  see  are  produced.  There  are  bodies  that  give  out 
such  waves  at  ordinary  temperatures.  Such  is  the  light 
from  decaying  wood  and  fish,  from  the  surface  of  the 
sea  when  stirred  by  a  passing  vessel  or  by  strong  Avind ; 
clouds  are  sometimes  luminous,  and  the  streamers  from 
meteors,  at  the  height  of  many  miles  where  the  temper- 
ature must  be  below  zero,  sometimes  last  for  several 
minutes.  Fireflies  and  glowworms  show  that  high 
temperature  is  not  essential  for  the  production  of  light 
waves.  They  also  give  out  X-rays  like  Crookes'  tubes. 
Such  luminosity  of  bodies  at  low  temperatures  is 
called  phosphorescence.  It  can  be  produced  artificially 


ETHER    WAVES.  267 

in  several  ways.  A  match  scratched  in  a  dark  room 
leaves  a  luminous  streak.  Certain  kinds  of  crystals, 
such  as  the  diamond  and  ruby,  give  out  light  only 
if  rubbed.  The  sulphides  of  calcium  and  barium  con- 
tinue to  shine  after  exposure  to  a  strong  light  for  a  few 
minutes,  and  a  kind  of  paint  has  been  made  of  the 
former  which  shines  for  hours  in  the  dark.  Electric 
discharges  make  glass  and  gases  luminous,  as  spoken 
of  on  page  183.  Such  phenomena  have  encouraged  the 
hope  that  light  for  commercial  and  household  purposes 
may  yet  be  produced  without  the  waste  of  energy  in 
the  shape  of  long  waves,  which  make  the  greater  part 
of  radiations  of  hot  bodies.  If  all  the  rays  from  an 
incandescent  electric  lamp  were  of  the  visual  length, 
the  lamp  would  give  out  twenty  times  more  light. 

Fluorescence.  —  If  a  little  quinine  be  dissolved  in  a 
test  tube  of  water  to  which  a  drop  of  sulphuric  acid  has 
been  added,  the  solution  will  appear  of  a  bright  blue 
color.  If  it  be  examined  in  the  colors  of  the  spectrum, 
it  will  not  show  this  color  in  either  the  red,  the  yellow, 
or  the  green  ;  in  the  blue  it  is  distinct,  and  will  con- 
tinue to  be  blue  when  moved  into  the  region  beyond 
any  of  the  visible  rays.  This  means  that  the  quinine 
possesses  the  property  of  changing  the  wave-lengths  to 
longer  ones.  Many  bodies  possess  this  quality  in  some 
degree,  but  a  few  have  it  in  a  remarkable  degree. 
Eosine,  uranine,  thaline  are  prepared  from  coal  tar. 
A  minute  quantity  of  either  of  these  dropped  upon  the 
surface  of  water  in  a  tumbler  will  be  seen  to  sink 
slowly,  leaving  a  beautiful,  deeply  colored  thread  from 


268  NATURAL    PHILOSOPHY. 

the  surface,  and  will  tinge  all  the  water.  If  this  water 
be  examined  in  the  spectrum  as  before,  the  particular 
colors  will  be  found  well  developed  in  rays  of  much 
shorter  wave-length  than  those  of  the  color  they  show. 
Their  molecules  in  some  way  act  so  as  to  increase  the 
wave-length  of  such  rays  as  are  reflected  by  them. 
Uranium  glass  which  has  a  yellowish  green  tint  is 
thus  fluorescent,  and  shows  its  colors  well  in  blue 
light;  also  when  lighted  up  by  an  electric  discharge. 
For  this  reason  that  kind  of  glass  is  sometimes  made 
into  vases  or  other  ornamental  forms  for  experiments 
with  electrical  discharges,  as  in  Geissler's  tubes.  Sub- 
stances that,  like  these,  change  the  wave-length  of  the 
rays  that  fall  upon  them  into  any  other  length  longer 
or  shorter  are  called  fluorescent  bodies.  The  above- 
mentioned  substances  all  lengthen  the  waves,  but 
naphthaline  red  in  red  light  reflects  yellow  light,  and 
chlorophane  changes  rays  below  the  red  of  the  spec- 
trum into  emerald  green  light.  It  is  a  remarkable  fact 
that  light  that  has  once  passed  through  a  fluorescent 
solution  will  not  affect  another  solution  of  the  same 
kind.  All  fluorescent  bodies  are  likewise  phosphorescent. 

QUESTIONS. 

1.  If  light  travels  186,300  miles  in  a  second,  how  long  will  it 
take  for  it  to  come  from  the  sun  to  the  earth  ? 

2.  If  it  takes  3^  years  for  light  to  come  to  us  from  the  nearest 
fixed  star,  how  far  away  is  it  ? 

3.  How  long  would  it  take  light  to  go  from  Boston  to  Chicago  ? 

4.  Suppose   a   straight   bar-magnet    like    a   compass     needle 
rotates   on    its   pivot   once    a   second ;    how   long   will    its  ether 
wave  be  ? 


ETHEll    WAVES.  269 

5.  If  it  should  spin  a  thousand  times   a  second,  how  long 
will  its  wave  be  ? 

6.  Two  lights  give  shadows  of  equal  intensity  on  the  photom- 
eter, —  one  is  one  foot  distant,  the  other  is  five  feet  distant  from 
the  surface  ;  how  much  brighter  is  one  than  the  other? 

7.  A  lens  has  a  focal  length  of  10  inches  ;  if  an  object  be 
placed  in  its  axis  15  inches  from  it,  how  far  on  the  other  side  of 

the  lens  will  the  image  be  ?     (-+1=1) 

8.  If  the  screen  (Fig.  117)  be  20  feet  from  the  lens  of  1-foot 
focus,  how  far  must  an  object  be  from  the  lens  to  produce  a  proper 
image  ? 

!».    How  large  would  be  the  image  of  a  nickel  coin  under  the 

above  conditions  ;  that  is,  how  much  would  be  the  magnification? 

10.    If  the  magnifying  power  of  a  lens  used  as  above  is  known 

to  be  250  diameters,  what    will  be  the  length  of  an  animalcule 

whose  image  is  found  to  be  four  inches  long  ? 


CHAPTER  XI. 
SOUND. 

THE  word  "  sound  "  is  sometimes  used  to  mean  the  sen- 
sation produced  through  the  ears  or  organs  of  hearing, 
and  sometimes  we  mean  by  sound  the  physical  disturb- 
ance in  the  air  that  may  produce  the  sensation  if  it 
reaches  the  ear.  The  former  is  called  the  physiological 
definition,  the  latter  the  physical  definition,  which  is 
the  one  to  be  considered  here.  By  listening  attentively 
one  may,  in  almost  any  place,  hear  a  number  of  differ- 
ent sounds  ;  as  those  of  a  ticking  clock,  of  buzzing 
flies,  the  wind,  bells,  or  whistles.  We  learn  to  distin- 
guish their  sources  and  direction,  but  need  to  call  to  our 
assistance  some  of  our  other  senses,  such  as  sight  and 
touch,  in  order  to  understand  what  takes  place  when 
the  sound  is  made. 

When  we  strike  the  table  with  the  knuckles  or  witli 
a  pencil,  there  is  heard  a  sound  of  short  duration  ;  but 
if  a  bell  or  a  tuning-fork  be  struck,  the  sound  continues 
for  some  seconds. 

Sounding  Bodies  are  Vibrating.  —  If  a  sounding 
bell  or  a  tuning-fork  be  touched  with  a  piece  of  paper, 
a  buzzing  sound  will  be  heard.  If  the  tuning-fork  be  a 
largo  one,  the  prongs  may  be  seen  swinging  to  and  fro. 
When  this  movement  is  no  longer  visible,  it  may  be 
made  apparent  again  by  swinging  the  fork  to  and  fro  in 


SOUND.  271 

a  bright  light ;  the  prongs  will  have  a  fan-shaped  appear- 
ance, which  will  be  lost  when  the  fork  stops  sounding. 
Let  the  end  of  the  thumb  be  dampened,  and,  holding  it 
nearly  vertical  on  a  table,  let  it  be  moved  rapidly  for- 
ward ;  the  vibration  of  the  thumb  will  be  plainly  felt 
and  the  sound  may  be  heard.  A  piece  of  chalk  upon 
the  blackboard  or  a  pencil  upon  a  slate  may  be  made 
in  like  manner  to  produce  a  sound,  and  a  line  of  dots 
will  indicate  how  many  times  the  moving  body  has 
touched  the  surface.  In  every  musical  instrument 
there  is  some  part  capable  of  prolonged  vibration,  — 
in  the  piano  and  harp,  the  wires  ;  in  the  parlor  organ, 
the  brass  reeds  ;  in  the  flute  and  cornet,  a  column  of 
air.  In  every  case  a  sounding  body  has  a  vibratory 
movement.  Sometimes  the  separate  vibrations  can  be 
distinguished,  as  when  the  thumb  is  pushed  across  the 
table,  but  generally  they  occur  so  frequently,  that  is, 
so  many  times  in  a  second,  that  the  ear  fails  to  distin- 
guish any  interval  between  them,  and  such  a  sound  is 
called  a  continuous  sound. 

If  a  wheel  having  teeth  like  a  cog-wheel  in  a  clock 
be  made  to  rotate,  and  the  edge  of  a  paper  card  be  held 
against  it,  one  may  determine  the  number  of  vibrations 
made  by  the  card  when  it  makes  the  lowest  continuous 
sound  ;  it  will  be  necessary  to  know  how  fast  the  wheel 
is  rotating,  and  how  many  teeth  there  are  in  the  wheel. 

Pitch.  —  With  the  above  device  one  may  observe 
another  fact :  as  the  wheel  turns  faster  the  sound  be- 
comes higher  and  higher  until  it  is  a  screech.  This 
change  in  the  sound  is  called  the  change  iir  pitch.  As 


272  NATURAL   PHILOSOPHY. 

the  card  vibrates  faster  the  pitch  rises,  and  as  its  rapid- 
ity diminishes  the  pitch  falls  until  the  individual  taps 
of  the  card  may  be  heard.  By  quickly  drawing  the 
finger  nail  across  the  cover  of  a  cloth-bound  book,  a 
sound  may  be  heard ;  its  pitch  will  depend  upon  how 
fast  the  finger  moves.  Tuning-forks  are  made  so  as  to 
vibrate  a  certain  number  of  times  a  second,  that  is, 
each  one  has  a  definite  pitch.  The  one  commonly  used 
for  experiment  is  called  a  C  fork,  and  makes  256  vibra- 
tions per  second.  Pianos  and  organs  are  tuned  to  a 
fork  making  261  vibrations  per  second  as  a  standard  ; 
the  middle  C  upon  the  keyboard  being  put  in  unison 
with  the  fork,  that  is,  made  to  have  the  exact  pitch  of 
the  fork  ;  the  remaining  keys  are  tuned  by  ear  from 
this.  By  pitch,  then,  is  meant  the  number  of  vibra- 
tions per  second  that  a  sounding  body  makes.  Thus 
the  pitch  of  the  lowing  of  a  cow  may  be  150  vibrations 
per  second,  a  locomotive  whistle  470,  the  chirp  of  a 
cricket  3000,  the  squeak  of  a  bat  5000  vibrations  per 
second. 

Energy  of  Sounds.  —  If  a  tuning-fork  be  struck 
hard  and  its  stem  be  pressed  upon  a  table,  it  will  give 
a  sound  of  a  certain  pitch  and  loudness,  but  in  a  few 
seconds  it  will  become  very  weak,  and  one  will  have  < 
to  listen  carefully  to  hear  it  at  all.  In  like  manner  the 
sound  will  be  very  weak  if  the  fork,  while  it  vibrates, 
be  held  in  the  hand  instead  of  upon  the  table,  yet  so 
long  as  it  can  be  heard  its  pitch  will  remain  the  same. 
One  may  sing  the  syllable  la  in  any  pitch,  softly  or 
loudly.  Difference  in  loudness  of  sounds  is  called 


SOUND.  273 

difference  in  intensity,  and  is  due  to  the  amount  of 
energy  spent  in  producing  the  air  vibrations.  When 
the  fork  is  first  struck,  the  movements  of  the  prongs 
may  be  seen,  and  the  sound  is  strong  ;  the  sound  be- 
comes weaker  as  the  ampUtittde  of  the  vibrations  (see  p. 
46)  becomes  less,  until  both  movement  and  sound  t-i-;i>c. 
The  loudness  of  sound  depends  upon  the  amplitude  of 
the  vibrations,  and  the  amplitude  depends  upon  the 
amount  of  vibratory  energy  the  body  has. 

Distributors  of  Sound.  —  Let  a  tuning-fork  be 
struck,  and  the  stem  be  touched  to  the  top  of  the  table 
three  or  four  times;  the  sound  is  much  louder  while 
the  stem  is  touching  the  table  than  when  it  is  held  in 
the  hand.  A  music  box  will  sound  louder  when  it  is 
placed  on  such  a  surface  than  when  held  in  the  hand. 
Let  a  pin  be  stuck  into  the  table  and  a  thread  tied  to 
it,  the  other  end  of  the  thread  being  tied  to  the  music 
box  or  the  fork;  if  the  box  or  fork  be  made  to  sound, 
the  loudness  will  be  much  increased  by  pulling  the 
thread  taut.  It  will  be  the  same  if  a  wire  or  a  wooden 
rod  be  used  to  connect  the  vibrating  body  with  the 
table,  which  shows  that  wood,  metal,  or  stretched 
strings  are  better  conductors  of  sound  than  air. 

If  the  ends  of  a  long  rod  or  wire  were  held  by  two 
persons,  and  one  should  pull  or  push  upon  it,  the  other 
would  feel  the  change.  When  it  is  remembered  that 
the  sounding  body  is  a  trembling  body,  it  may  be  per- 
ceived why  the  trembling  motions  are  transferred  or 
conducted  away.  The  condition  for  such  conduction 
is  that  the  conductor  be  elastic,  and  the  higher  the 


274  NATURAL    PHILOSOPHY. 

degree  of  elasticity,  the  faster  the  sound  is  conducted 
away.  If  the  sound  is  conducted  away  faster,  it  is 
plain  that  the  sounding  body  must  be  losing  energy 
faster.  With  a  clock  or  watch  in  sight,  strike  a  tuning- 
fork,  and,  holding  it  in  the  fingers,  note  how  many 
seconds  it  can  be  heard.  It  may  be  gently  touched 
to  the  table  once  in  four  or  five  seconds  to  increase  the 
strength  of  the  sound.  Make  the  fork  sound  as  before, 
and  hold  the  stem  upon  the  table  all  the  time ;  it  will 
not  be  heard  as  long. 

In  the  absence  of  elastic  bodies,  sound  cannot  be 
conducted  away  at  all.  The  air  is  an  elastic  body,  and 
serves  to  distribute  sound  in  every  direction.  If  a 
sounding  body  like  a  bell  be  placed  in  a  good  vacuum, 
it  cannot  be  heard  ;  the  whole  energy  of  the  sound  is 
transformed  into  heat  and  raises  the  temperature  of  the 
bell. 

Sound  Waves.  —  Suppose  the  open  hand  be  swung 
to  and  fro  like  the  prong  of  a  tuning-fork  ;  as  the  hand 
moves  forward,  the  air  in  front  of  it  is  condensed  while 
the  air  behind  it  is  rarefied.  The  denser  air  has  greater 
pressure  than  the  more  rarefied  air,  and  this  difference 
in  pressure  causes  movements  in  the  air  towards  the 
place  where  the  pressure  is  less.  The  rate  at  which 
such  a  disturbance  in  the  air  travels  is  several  hundred 
feet  in  a  second.  The  hand  moves  so  slowly  that  the 
difference  in  pressure  is  very  slight  and  is  equalized 
almost  instantly.  If  the  hand  could  move  fast  enough 
;i  perfect  vacuum  would  be  formed  behind  it,  and  if  it 
could  swing  to  and  fro  fast  enough  it  would  maintain  a 


SOUND.  275 

space  nearly  free  from  air  on  both  sides  of  it.  A  con- 
densation in  the  air  immediately  begins  to  travel  in 
every  direction,  as  a  wave  started  in  water  travels  in  a 
widening  circle.  The  same  is  true  of  a  rarefaction  in 
the  air.  A  vibrating  body  forms  a  condensation  when 
moving  forwards,  and  a  rarefaction  on  the  same  side 
when  moving  backwards ;  both  move  outwards  in  every 
direction,  and  together  they  constitute  a  sound  wave. 

The  length  of  a  sound  wave  is  the  distance  from  the 
middle  of  one  condensation 
to  the  middle  of  the  next, 
and,  therefore,  represents  a 
complete  to-and-fro  move- 
ment of  the  vibrating  body. 
The  fork  vibrates  a  great 

many  times  a  second,  and  a  wave-length  depends 
upon  how  far  the  first  condensation  has  traveled  while 
the  remainder  of  the  wave  is  being  completed.  The  air 
being  composed  of  molecules,  it  does  not  move  in  a 
body,  but  each  molecule  moves  towards  and  away  from 
the  source  of  the  sound.  The  molecules  are,  therefore, 


more  crowded  in  some  parts  of  the  line  than  in  others. 
Such  a  vibration  is  called  a  longitudinal  vibration.  As 
;in  illustration  of  this  kind  of  wave  motion,  take  two 
combs  having  different  n umbel's  of  teeth  to  the  inch, 
for  example,  one  with  fifteen  and  the  other  with  twelve  ; 
place  the  combs  together,  and,  holding  them  at  arm's 
length  towards  a  window,  slowly  slide  one  over  the 


276  NATURAL   PHILOSOPHY. 

other;  series  of  dark  and  of  light  spaces  will  be  seen  to 
move  regularly  after  each  other.  If  the  dark  space  be 
likened  to  the  dense  part  of  the  sound  wave,  while  the 
light  space  answers  for  the  rarefied  part,  the  motions 
will  be  exactly  like  those  of  sound  waves.  The  same 
thing  may  be  seen  often  while  looking  from  a  distance 
through  a  picket  fence  at  another  one  behind  it.  If 
the  observer  be  moving,  series  of  light  and  dark  bands 
will  follow  each  other  like  sound  waves.  Air  is  so 
transparent  that  it  cannot  be  seen,  and  waves  in  it  can- 
not be  seen,  but  air  waves  may  be  felt.  Let  one  stand 
one  or  two  hundred  feet  distant  from  a  cannon  when  it 
is  fired,  the  wave  of  dense  air  as  it  passes  will  be  felt 
as  a  swift  wind.  Let  a  piece  of  stout  paper  be  tied 
over  the  flaring  end  of  a  funnel,  and  the  paper  be 
snapped  with  thumb  and  finger  while  the  small  end  is 
directed  towards  the  face,  the  puff  produced  will  be 
plainly  felt,  and  if  directed  towards  a  lighted  candle,  the 
latter  may  be  puffed  out  even  at  the  distance  of  eight 
or  ten  feet.  The  air  is  condensed  within  the  funnel, 
and  the  condensation  escapes  at  once,  by  way  of  the 
throat.  A  series  of  strokes  will  give  a  series  of  conden- 
sations which  will  follow  each  other  like  sound  waves. 

The  amplitude  of  the  vibratory  movement  of  most 
sounding  bodies  is  very  small  indeed.  A  tuning-fork 
may  give  a  loud  sound  and  still  appear  quiescent  to 
the  eye,  the  actual  displacement  of  the  prong  being 
less  than  the  ten-thousandth  of  an  inch.  The  move- 
ment of  the  air  particles  is  even  less.  When  it  is 
remembered  that  sound  can  be  heard  in  every  direction 
from  a  sounding  body,  and  that  the  energy  of  the  waves 


SOUND.  277 

is  rapidly  diffused  to  larger  and  larger  bodies  of  air, 
it  will  be  understood  that  the  actual  motion  of  an  air 
molecule  when  the  sound  is  at  the  distance  at  which 
one  can  hear  another  person  whistle  —  say  1000  feet 
—  must  be  measured  in  millionths  of  an  inch ;  for  it 
need  be  no  more  than  the  hundredth  of  an  inch  at  the 
starting  point,  and  the  intensity  varies  inversely  as  the 
square  of  the  distance  from  that  point.  Such  a  small 
distance  is  comparable  with  the  magnitude  of  the  mole- 
cules themselves. 

Velocity  of  Sound.  — There  is  a  noticeable  difference 
in  time  between  seeing  the  flash  of  a  distant  gun  and 
hearing  the  report.  A  bursting  rocket  and  a  flash  of 
lightning  are  followed  by  sounds  after  an  interval  of 
time,  the  length  of  which  depends  chiefly  upon  the 
distance  of  the  disturbance  from  the  observer.  Careful 
experiments  have  shown  that  the  velocity  of  sound  in 
air  varies  with  the  temperature.  At  the  temperature 
of  freezing  water,  that  is,  at  32°  F.,  the  velocity  is 
1090  feet  per  second,  and  increases  about  one  foot  per 
second  for  every  degree  higher,  so  that  at  70°  F.  it  is 
1090  -f  38  =  1128  feet  per  second.  The  distance  of  a 
flash  of  lightning  may  be  roughly  estimated  by  allowing 
five  seconds  for  a  mile.  It  is  rather  remarkable  that 
thunder,  though  often  very  loud,  can  seldom  be  heard 
more  than  five  or  six  miles,  while  cannon-firing  and 
powder-mill  .explosions  have  been  heard  fifty  or  more 
miles.  The  reason  for  this  difference  is,  probably,  that 
the  thunder  is  altogether  in  the  air,  while  the  others 
are  upon  the  earth  and  shake  it  directly. 


278  NATURAL   PHILOSOPHY. 

All  kinds  of  sounds  travel  with  the  same  velocity. 
Hence  the  velocity  depends  only  upon  the  properties 
of  the  air,  not  upon  the  source  or  the  pitch  of  the 
sound. 

Wave-Lengths  of  Sound.  —  Suppose  a  tuning-fork 
make  100  vibrations  per  second.  At  the  end  of  the 
first  second  the  first  wave  formed  would  have  traveled 
a  distance  equal  to  the  velocity  of  sound  at  that  tem- 
perature, and  between  the  first  wave  and  the  last  one 
there  would  be  a  line  of  100  waves  —  all  alike  and  of 
the  same  length.  If  the  velocity  were  1125  feet  per 
second,  each  wave  would  be  ^-^-  =  11.25  feet  long. 


Let  v  =  velocity  of  sound  in  air, 

n  =  number  of  vibrations  per  second, 
I  =  wave-length  ;    then 


I  —  —  and  v  =  nl. 


Given  any  two  of  these  factors,  the  other  can  be  calcu- 
lated. 

The  velocity  of  sound  is  much  greater  in  liquids  and 
solid  bodies  than  in  air,  for  their  elasticity  is  greater. 

Sound  travels  in  water  4  times  as  fast  as  in  air. 

«           «         «  brass  10  "  "  "  "  "  " 

«           «         «  copper  12  "  "  "  "  "  " 

«  steel  16  »  «  «  "  «  « 

"          "         «  oakwood  10  "  "  "*  "  "  " 

«  birch  14  «  «~  «  "  «  « 

"           "         "  pine  or  spruce   18  "  "  "  "  "  " 

«          »         «  glass  16  "  "  "  "  "  " 


SOUND.  279 

Thus  it  appears  that  sound  has  a  velocity  greater  than 
three  miles  a  second  in  a  steel  wire,  and  sound  waves 
that  would  be  ten  feet  long  in  air  would  be  160  feet 
long  in  such  a  wire. 

Speaking-  Tubes.  —  The  sound  waves  produced  by 
the  voice  begin  at  the  mouth  to  scatter  in  every  direc- 
tion, and  every  one  in  a  large  hall,  or  at  a  great  distance 
in  an  open  field,  may  hear,  but  the  sound  is  weaker  and 
less  distinct  at  a  distance,  for  the  energy  of  the  part 
that  reaches  the  ear  is  less.  If  one  speaks  into  a  long 
tube  or  pipe,  it  is  not  possible  for  the  sound  waves  to 
be  diffused  as  they  are  when  in  the  open  air  ;  they 
retain  their  energy  for  a  longer  time  and  may  be  heard 
at  a  much  greater  distance.  Conversation  even  in 
whispers  has  been  carried  on  through  empty  water 
pipes  more  than  a  half  mile  long.  The  common  speak- 
ing tubes  used  in  houses  to  communicate  between  dis- 
tant rooms  direct  the  sound  waves  without  diffusing 
them. 

The  String  Telephone.  —  If  one  will  talk  or  sing 
into  a  tin  cup,  or  similar  vessel,  he  will  be  able  to  feel 
the  vibratory  motions  of  the  bottom  of  the  cup  by 


FIG.  151.  —  The  String  Telephone. 

touching  it  with  a  finger.  The  air  waves  make  the 
bottom  swing  to  and  fro  as  many  times  as  there  are 
waves  to  act  upon  it.  If  two  such  cups  be  connected 
together  by  a  string  fastened  to  the  middle  of  the  bot- 


280  NATURAL   PHTLOSOPHY. 

torn  of  each,  one  may,  by  holding  one  cup  to  the  ear, 
hear  easily  what  another  speaks  into  the  other  cup, 
even  at  the  distance  of  a  thousand  feet,  provided  the 
string  be  kept  taut. 

In  this  case  the  vibrations  of  the  bottom  of  the  cup 
give  longitudinal  vibrations  to  the  string  or  wire  which 
connects  it  with  the  other,  and,  in  turn,  the  bottom  of 
the  second  cup  is  made  to  vibrate  in  the  same  way  as 
the  first.  The  waves  are  in  the  string,  and  therefore 
are  not  diffused  like  air  waves,  and  may  be  transferred 
to  a  greater  distance.  If  the  string 
or  wire  touch  a  body  like  a  tree  or  a 
house,  the  sounds  will  be  stopped.  If 
an  angle  is  made  in  the  direction  of 
the  string,  the  latter  must  be  held  in 
position  by  another  string  A  a  few 
inches  long  (Fig.  152).  Let  one  cup  be  detached  and 
the  end  of  the  string  be  fastened  to  a  pin  stuck  in  a 
panel  of  the  door,  and  a  person  may  hear  a  whisper 
made  so  gently  in  the  cup  that  no  one  in  the  room 
could  hear  it  at  all.  This  means  that  the  whole  door 
is  made  to  vibrate  in  the  same  way  that  the  bottom  of 
the  cup  vibrates,  and  that,  too,  when  the  sounds  are  only 
faint  whispers. 

In  like  manner  two  persons  may  communicate  in 
whispers  through  a  closed  door,  one  listening  with  ear 
against  the  door,  and  the  other  speaking  to  the  opposite 
side. 

With  the  mouth  close  to  the  door  or  to  a  wall,  the 
energy  of  the  air  vibrations  will  be  mostly  spent  upon 
the  small  surface;  at  a  greater  distance  the  energy  will 


SOUND.  281 

diffuse  itself  through  the  room,  and  the  walls,  floor, 
and  ceiling  will  receive  only  a  proportional  part,  and 
will  be  made  to  vibrate  correspondingly.  The  larger  the 
space,  the  less  will  be  the  energy  to  the  square  indi. 
Whether  more  or  less,  it  acts  in  the  same  way  on  every 
elastic  surface,  and  every  object  in  the  room,  whatever 
its  size,  is  made  to  vibrate  by  every  sound.  If  the 
walls  of  the  room  are  thus  made  to  shake,  the  house  is 
shaken,  and  the  earth  in  turn  has  the  position  of  every 
molecule  in  it  changed  in  some  degree  by  the  energy 
of  sounds.  When  the  vibrations  are  of  molecular  mag- 
nitudes we  call  them  heat,  and  sound  waves  are  all 
ultimately  resolved  into  heat,  and  are  mostly  radiated 
away. 

FORCED  AND  SYMPATHETIC  VIBRATIONS. 

Every  Elastic  Body  has  some  Vibratory  Rate  or 
Pitch.  —  When  a  load  of  stones  is  tipped  out  of  a  cart, 
the  sound  is  called  a  noise.  It  is  a  kind  of  roar  with- 
out any  particular  pitch;  but  if  each  stone  be  struck 
with  a  small  hammer,  it  will  be  heard  to  give  a  sound 
having  a  definite  pitch.  Stones  of  different  sizes  and 
shapes  give  different  pitches,  so  that  it  is  not  difficult 
to  select  a  series  that  will  give  the  whole  musical  scale. 
Pieces  of  wood,  large  nails,  bolts,  and  the  like  will  each 
give  out,  if  free,  a  particular  sound  when  struck,  as 
well  as  an  iron  poker,  a  glass  tumbler,  or  a  piano-string. 

When  sound  waves  in  the  air  fall  upon  a  body  which 
has  the  same  vibratory  rate  as  the  waves,  the  body  is 
not  only  made  to  vibrate,  but  each  air  wave  makes  it 


282  NATURAL    PHILOSOPHY. 

vibrate  a  little  further,  and  so  its  amplitude  is  increased, 
just  as  slight  pushes  upon  one  in  a  swing  will  cause 
the  swing  to  go  further  and  further,  and  continue  to 
swing  for  some  time  after  the  pushing  stops.  With 
the  voice  get  the  pitch  of  any  key  on  the  piano,  then 
with  that  key  pressed  down  sing  that  note  to  any  syl- 
lable. On  stopping,  the  piano  will  be  heard  to  give 
out  the  same  note,  though  it  has  not  been  struck.  The 
air  vibrations  have  set  it  in  motion.  A  different  key 
pressed  down  will  give  no  response.  Such  an  instru- 
ment as  a  bass  viol,  even  if  it  be  many  feet  distant,  may 
be  made  to  respond  loudly  by  sounding  with  the  voice 
the  pitch  of  any  of  the  strings.  Two  tuning-forks  of 
the  same  pitch  act  thus  on  each  other ;  either  will  cause 
the  other  to  vibrate  by  the  impact  of  its  air  waves. 
Such  forks  are  called  sympathetic  forks ;  and  vibrations 
that  cause  another  body  having  the  same  pitch  to 
vibrate  are  called  sympathetic  vibrations. 

Press  down  the  damper  pedal  of  a  piano  so  as  to  free 
all  the  strings,  and  then_sing  or  speak  or  make  any 
kind  of  a  sound,  and  the  strings  will  at  once  respond 
loudly.  There  are  so  many  strings  with  so  many  dif- 
ferent pitches  that  it  makes  little  difference  what  pitch 
is  chosen;  there  will  be  some  strings  in  unison  with  it, 
and  they  will  be  set  vibrating  sympathetically. 

If  a  body  having  a  definite  rate  of  vibration  is  made 
to  vibrate  at  some  different  rate,  such  vibrations  are 
called  forced  vibrations.  Thus,  when  the  stem  of  a 
vibrating  tuning-fork  is  held  upon  the  table,  the  latter 
sounds  loudly,  but  the  rate  of  vibration  of  the  fork  is 
not  the  same  as  the  pitch  of  the  table,  as  the  table  will 


SOUND. 


283 


respond  in  the  same  way  for  a  fork  of  any  pitch.  The 
sounding  boards  of  pianos  and  the  shells  of  violins  are 
thrown  into  forced  vibrations  by  the  sounding  strings, 
and  thus  the  sounds  are  distributed  to  a  much  greater 
body  of  air,  the  strings  losing  their  energy  at  a  swifter 
rate. 

Resonance.  —  Tuning-forks  for  experimental  work 
are  often  mounted  on  boxes  open  at  one  or  both 'ends 
(Fig.  153).  When  such  forks  are  struck,  they  sound 


very  much  louder  and  can  be  longer  heard;  but  if  the 
hand  be  placed  over  the  open  end,  the  sound  is  greatly 
lessened.  If  the  fork  be  removed  from  the  box  and 
the  prongs  be  held  in  front  of  the  open  end  of  the  box. 
the  sound  will  be  nearly  as  loud  as  when  the  fork 
rested  upon  the  box.  Another  fork  with  a  different 
pitch  requires  a  box  of  a  different  size  to  respond  in 
like  manner.  A  pocket  tuning-fork,  if  made  to  vibrate 
and  held  over  the  end  of  a  tube,  as  a  lamp  chimney, 
may  not  be  heard  any  more  plainly;  but  if  the  tube  be 
plunged  into  water  so  as  to  shorten  the  column  of  air 


284  NATURAL   PHILOSOPHY. 

in  it  (Fig.  154),  some  length  above  the  water  can  readily 
be  found  where  the  sound  will  be  greatly  reinforced. 
The  phenomenon  is  called  resonance,  and  such  tubes 
are  called  resonant  tubes  or  boxes.  The  explanation  of 
this  is,  the  column  of  air  has  the  same  rate  of  vibration 
as  the  fork;  that  is,  it  vibrates  sympathetically.  When 
the  prong  of  the  fork  beats  downward,  forming  a  con- 
densation, the  condensation  travels  down  the  tube  and 
is  reflected  from  the  bottom  to  the  top ;  if  it  gets  back  to 
the  top  at  the  same  time  the  prong  gets  to  its  normal 
position,  the  rarefication  begins  to  form  at  the  fork, 
travels  down  the  tube,  and  is  -reflected  from  the  bottom 
as  the  condensation  was,  getting  back  to  the  top  of  the 
tube  when  the  prong  reaches  its  normal  position  again; 
so  for  each  complete  vibration  of  the  fork,  both  parts 
of  the  air  wave  travel  twice  the  length  of  the  tube, 
—  for  the  complete  wave,  four  times  the  length  of  the 
tube.  It  follows  that  the  length  of  the  air  wave  is  four 
times  the  length  of  the  tube  that  responds  to  it.  In 
this  way  one  may  determine  how  many  times  a  fork 
vibrates  in  a  second:  find  what  length  of  tube  is  required 
for  strongest  resonance;  four  times  that  will  be  the 
wave-length  I  of  that  sound.  Ascertain  the  tempera- 
ture in  order  to  know  what  the  velocity  v  of  sound  is 

at  that  place;  then  -  =  ?i,  the  number  of  vibrations  made 

by  the  fork.  If  the  tube  be  a  broad-mouthed  one,  it 
will  be  necessary  to  add  to  the  measured  length  of  the 
tube  about  two-thirds  of  the  diameter  of  the  mouth  for 
one-fourth  the  wave-length.  For  example,  a  tube  an 
inch  and  a  half  in  diameter  and  twelve  inches  long  was 


SOUND.  285 

found  to  respond  loudest  to  a  fork.  What  was  the 
pitch  of  the  fork,  the  temperature  being  70°  F.  ? 

v  =  1090+38  =  1128  feet. 

1  =  4  (12  +  1)=  52  inches  =  41  feet. 

-  = — -T^ —         =  260  =  n.     260  vibrations  per  second. 

In  like  manner  one  can  determine  the  velocity  of  sound 
in  air  by  knowing  how  many  times  a  given  fork  vibrates, 
and  measuring  the  wave-length  in  the  above  way,  for 
nl=  v. 

The  resonance  of  columns  of  air  is  the  chief  source 
of  sound  in  wind  instruments,  such  as  flutes,  organ- 
pipes,  and  cornets.  The  holes  in  the  flute  and  the 
valves  in  the  cornet  regulate  the  length  of  the  column 
of  resonant  air ;  the  pitch  of  the  organ-pipe  depends 
upon  its  length,  and  is  constant.  The  mouth  is  a  good 
resonator  for  a  tuning-fork;  by  varying  the  size  of  the 
cavity  one  may  find  by  trial  a  size  that  will  respond  so 
as  to  be  heard  fifty  feet  away.  By  snapping  the  cheek 
with  the  finger,  the  resonance  of  the  mouth  may  be 
heard,  and  a  tune  may  be  played  by  varying  its  size. 
For  sounds  that  have  a  lower  pitch,  such  as  those 
of  the  voice  of  a  man,  which  have  a  wave-length  of 
eight  or  ten  feet,  the  resonant  tube  must  be  correspond- 
ingly larger  and  longer.  Places  are  often  found  in 
halls,  in  long  archways,  and  in  some  caverns  where  the 
voice  at  a  certain  pitch  causes  a  very  loud  response. 
The  amplitude  of  the  air  vibrations  is  made  many  fold 
greater  by  such  conditions. 


286  NATURAL   PHILOSOPHY. 

Echo.  —  Sound  waves  are  reflected  from  any  sur- 
face in  the  same  way  they  are  from  the  bottom  of  a 
resonant  tube.  The  tube  serves  merely  to  keep  the» 
vibrations  from  spreading  in  every  direction.  Such 
reflected  sounds  are  called  echoes,  and  are  often  heard 
from  buildings  or  hills  not  too  distant.  At  the  dis- 
tance of  75  or  100  feet  from  a  building  shout  "  Holloa ! " 
or  clap  the  hands  together,  and  the  return  sound 
may  be  plainly  heard.  The  echo  of  bells,  whistles, 
and  other  sounds  is  common  enough,  but  one  seldom 


or  never  hears  an  echo  from  the  clouds.  When  sound 
waves  rising  in  the  air  meet  an  air  surface  where  the 
wind  is  blowing  in  some  different  direction  from  that 
in  which  the  sound  has  been  moving,  they  are  deflected, 
and  may  be  directed  to  the  surface  of  the  earth. 

This  is  frequently  noticed  near  coasts  where  fog-horns 
are  blown  as  warning  signals  to  vessels.  Sounds  made 
at  c  (Fig.  155)  are  tilted  upwards  by  the  wind  a,  so  as 
to  leave  a  space  at  a  sometimes  a  mile  or  two  wide, 
within  which  they  cannot  be  heard,  though  audible  at 
a  greater  distance  d. 

Vibration  of  Strings.  —  If  a  piece  of  twine  or  thread 
twelve  or  fifteen  inches  long  be  stretched  and  then 
plucked  with  the  finger,  it  will  be  heard  to  give  out  a 


SOUND.  287 

sound;  the  tighter  it  is  stretched,  the  higher  the  sound 
it  will  make.  The  difference  in  pitch  may  be  so  great 
for  the  difference  in  tension  that  may  be  given  by  the 
hand  that  a  tune  may  be  plucked  on  the  string  by  one 
having  a  correct  ear.  The  timing  of  guitars,  violins, 
and  pianos  consists  in  giving  the  proper  tension  to  the 
strings. 

A  sonometer  (Fig.  156)  is  an  instrument  for  the  study 
of  the  relations  of  the  tension,  length,  size,  and  weight 
of  strings  to  their  pitch.  It  is  about  forty  inches  long, 


and  generally  has  two  wires  stretched  between  its 
bridges.  These  may  be  tuned  like  the  wires  of  a  piano. 
There  is  also  a  movable  bridge,  so  the  vibrating  part  of 
either  wire  can  be  varied  at  will.  With  this  instru- 
ment one  can  discover 

1.  That  the  number  of  vibrations  a  cord  or  wire  will 
make  is  inversely  as  its  length. 

2.  The  pitch  varies  with  the  tension. 

3.  "       "          "      inversely  as  the  diameter. 

4.  "       "          "  "          "    "    density. 

In  the  stringing  of  a  violin  or  of  a  piano  these  laws 
are  observed.  For  instance,  on  the  violin  all  four  of  the 
strings  have  the  same  length;  for  the  highest  sounds 
a  string  of  small  diameter  is  employed,  while  for  the 
lowest  sounds  a  larger  one  is  used,  wound  with  fine 


288  NATURAL   PHILOSOPHY. 

wire  to  give  it  greater  density,  and  the  intermediate 
strings  vaiy  in  diameter.  In  the  piano  the  wires  vary 
in  length,  tension,  and  diameter.  The  lowest  ones  are 
not  the  longest,  but  they  are  much  thicker  —  sometimes 
are  as  much  as  a  quarter  of  an  inch  in  diameter.  The 
upper  wires  are  both  short  and  fine.  A  good  example 
of  the  conditions  that  affect  a  vibratory  body  may  be 
shown  by  stretching  a  strip  of  India  rubber,  and  making 
it  give  out  a  sound  while  its  tension  is  being  varied. 
It  will  be  found  to  give  out  the  same  pitch,  whatever 
the  tension,  for  as  it  is  stretched  its  diameter  is  propor- 
tionately lessened. 

Compound  Vibrations. — Let  a  rope  fifteen  or  twenty 
feet  long  be  fastened  at  one  end  to  the  wall,  while  the 
other  end  is  shaken  by  the  hand.  By  properly  timing 
the  shakes,  the  rope  may  lie  made  to  swing  as  a  whole, 
as  at  A  in  Fig.  157.  A  faster  movement  of  the  hand 
will  cause  it  to  break  up  into  two  parts  called  scipnents^ 
as  at  B ;  and  still  faster  movement  will  break  it  into 
three  segments,  as  at  C.  In  B  and  C  there  are  points 
where  there  is  apparently  no  movement,  as  at  n.  These 
points  are  called  nodes.  By  employing  a  large  tuning- 
fork  in  the  place  of  the  hand  and  a  long,  stout  thread. 
one  may  observe  as  many  as  fifteen  or  twenty  such 
segments  on  the  thread,  the  number  depending  on  the 
tension  employed.  The  experiment  shows  that  a  string 
may  vibrate  in  parts  as  well  as  a  whole.  A  stretched 
wire  will  vibrate  in  a  similar  way.  Tune  both  wires 
on  the  sonometer  to  the  same  pitch,  and  place  the  slid- 
ing bridge  under  one  of  them  so  as  to  divide  the  wire 


SOUND. 


289 


into  two  equal  parts;  each  half  on  being  plucked  will 
give  the  same  sound.  Place  a  small  paper  rider,  made 
by  folding  a  piece  of  paper  two  inches  long  and  a 
quarter  of  an  inch  wide,  so  it  will  straddle  the  long 
wire  at  its  middle.  If  the  short  wire  be  plucked,  the 
rider  will  remain  in  place  ;  but  if  the  rider  be  put  else- 
where on  the  long  wire,  it  will  be  thrown  off.  By  mak- 
ing several  such  riders  and  placing  them  at  different 


places  on  the  long  wire,  all  will  jump  off  except  the  one 
at  the  middle  point  where  there  is  a  node.  The  long  wire 
vibrates  sympathetically  with  the  shorter  one,  and  this 
necessitates  a  node  at  its  middle  point.  If  the  bridge 
be  moved  to  one-third  the  length  of  the  wire,  and  this 
wire  be  plucked,  the  paper  riders  on  the  long  wire  will 
indicate  by  their  movements  that  it  has  three  vibrating 
parts  and  two  nodes,  like  C  (Fig.  157).  These  vibrations 
of  the  long  wire  will  be  too  minute  to  be  seen,  but  are 
sufficiently  energetic  to  toss  the  papers  and  thus  show 
how  the  wire  vibrates.  Also,  one  may  hear  the  pitch 
of  the  long  wire  when  thus  made  to  vibrate  sympatheti- 


290  NATURAL   PHILOSOPHY. 

cally  with  the  shortened  length  of  the  other  wire,  but  it 
will  be  needful  to  stop  the  vibrations  of  the  short  wire,  by 
touching  it  with  the  finger  after  two  or  three  seconds. 

A  stretched  string  or  wire  may  vibrate  in  more  than 
one  period,  and  produce  sounds  of  more  than  one  pitch. 
By  plucking  the  wire  of  a  sonometer  in  different  places 
one  may  notice  the  different  sounds  it  gives;  some  of 
them  may  be  very  high. 

One  may  now  notice  the  different  sounds  which  are 
given  out  by  many  bodies,  — a  tuning-fork  struck  with 
a  piece  of  metal,  an  iron  rod  struck  with  a  piece  of 
wood  and  with  a  hammer.  The  different  sounds  which 
a  violin  can  give  in  the  hands  of  an  unskillful  player 
are  well  known,  and  a  piano-string  sounds  very  different 
when  plucked  with  the  finger  than  when  struck  by 
its  proper  hammer.  A  piece  of  stout  thread  stretched 
between  two  tacks  a  foot  or  two  apart  in  the  window 
sill,  close  to  the  sash,  will  make  many  pleasant  musical 
sounds  if  the  sash  be  raised  about  an  inch  so  the  wind 
may  blow  in  past  the  thread.  The  device  is  called  an 
Aeolian  harp.  The  thread  breaks  up  into  many  seg- 
ments, each  one  producing  its  own  pitch;  all  are  heard 
together  and  are  highly  musical. 

The  lowest  sound  that  a  stiing  or  other  sounding 
body  makes  is  called  its  fundamental  pitch,  and  the 
other  sounds  are  called  overtones  or  harmonics. 

Analysis  of  Sounds.  —  With  a  well-tuned  piano 
one  may  discover  what  sounds  are  present  in  its  longer 
wires  by  their  sympathetic  effects  on  the  upper  ones. 
Thus,  gently  press  down  the  upper  G  key  of  the  bass 


SOUND. 


291 


clef  (Fig.  158),  so  as  not  to  strike  the  hammer ;  then 
strongly  strike  the  lower  G,  let  it  sound  a  second  or 
two,  and  then  let  it  up;  the  upper  G  will  be  heard 
sounding  loudly,  showing  that  the  lower  G  had  that 
component  in  it.  The  D  above  the  G  will  also  be  made 
.-  m  — |  to  vibrate  if  held  in  the  same  way  while 
p3z  ^  Eq  the  lower  G  is  struck.  In  this  way  one 
may  trace  the  vibrations  of  the  lower  G 
to  the  keys  above  (Fig..  159). 

In  like  manner,  by  holding  down  the 
lower  G  key  while  the  upper  keys  are 
struck  one  at  a  time,  each  one  will  cause 
the  long  wire  to  give  out  the  pitch  of 
the  one  struck,  as  illustrated  with  the 
sonometer. 

Another  method  of  analyzing  sound  is  based  upon 
the  property  of  resonance.  Instead  of  making  the  boxes 
like  those  adapted  for  tuning-forks,  as  described  on 
page  283,  they  may  be  made  spherical,  with  an  opening 
on  one  side  for  the  sound  waves  to 
enter  and  a  small  projection  on  the 
opposite  side  to  be  placed  in  the  ear 
(Fig.  160).  Such  a  resonator  of  a 
proper  size  will  respond  to  only  one 
given  pitch,  and  a  series  of  differ- 
ent sizes  will  enable  one  to  detect 
the  presence  of  overtones  in  sounds  of  musical  instru- 
ments and  of  the  voice.  With  such  means  it  has  been 
found  that  there  are  few  sounds  which  are  simple,  that 
is,  consist  of  only  a  single  rate  of  vibration.  A  tuning- 
fork  upon  its  resonance  box  is  nearly  so. 


FIG.  160. 


292 


NATURAL   PHILOSOPHY. 


Most  sounds  are  highly  complex,  and  their  several 
constituents  usually  stand  in  a  certain  numerical  rela- 
tion to  each  other,  such  that  the  first  overtone  above 
the  fundamental  or  pitch  is  made  by  twice  as  many 
vibrations  as  the  fundamental,  the  second  by  three 


INSTRUMENTS. 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

K 

3' 

c 

1 

Fl 

V 

r 

IX 

C9 
ft 
0 

Wide  stopped 
Narrow  stopped 
Narrow  cylinder 
Principal^  Wood) 
Conically  tiarrow  at  top, 
ute  
olin  
ano  
sll  
arionet  

/ 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

issoon 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

tx>e  

/ 

/ 

/ 

/ 

/ 

/ 

/ 

times  the  fundamental,  and  so  on;  thus,  if  the  funda- 
mental or  lowest  sound  is  made  by  100  vibrations,  the 
first  overtone  will  be  made  by  200,  the  second  by  300, 
the  third  by  400,  the  fourth  by  500,  and  so  on,  up  to 
the  twentieth  and  beyond.  One  hears  these  all  together, 
and  unless  one  has  listened  for  them,  they  may  never 
have  been  noticed,  and  they  may  have  been  thought  of 


SOUND.  293 

altogether  as  of  a  single  sound.  Listen  to  a  distant 
church-bell,  and  two  or  three  different  sounds  may  be 
detected. 

All  the  above-mentioned  constituents  are  not  present 
in  all  sounds,  but  when  present  they  are  in  these  ratios. 
Also,  when  present,  some  constituents  are  relatively 
stronger  than  others,  and  this  difference  in  the  nuniU-r 
and  strength  of  the  overtones  is  what  makes  the  differ- 
ence in  the  character  or  quality  of  the  sounds  of  musical 
instruments,  such  as  the  piano,  the  flute,  and  the  violin. 

The  accompanying  table  gives  the  composition  of 
the  tones  of  a  number  of  common  musical  instruments. 
The  heavy  lines  in  column  1  represent  the  fundamental 
sound  or  pitch  of  the  instrument;  the  lighter  ones  in 
the  other  columns  represent  the  overtones  present. 
Thus  in  the  flute,  besides  the  fundamental,  the  second, 
third,  and  fourth  in  the  series  are  present.  The  clari- 
onet has  for  overtones  the  third,  fifth,  seventh,  and 
ninth;  and  the  violin  has  the  whole  series,  though  the 
eighth,  ninth,  and  tenth  are  weaker  sounds  than  the 
others,  and  are  indicated  by  lighter  lines. 

The  Voice.  —  No  two  voices  are  alike.  All  of  us 
can  distinguish  the  voices  of  our  acquaintances,  whether 
the  persons  can  be  seen  or  not,  as  readily  as  we  can 
distinguish  the  sound  of  different  musical  instruments. 

The  vocal  organs  in  man  are  highly  complex  in 
structure,  made  up  of  bones,  cartilage,  muscles,  tubes, 
and  cavities  of  variable  size.  The  air  enters  the  lungs 
through  the  mouth  and  nose  cavities  M  and  C  (Fig.  l(i^). 
thence  through  a  special  device  called  the  larynx  G, 


294 


NATURAL    PHILOSOPHY. 


into  a  tube  called  the  trachea,  which  branches  into 
smaller  tubes  called  bronchial  tubes  in  the  lungs.  The 
sound-producing  organ  consists  of  two  cartilages,  which, 
like  two  lips,  nearly  close  the 
opening  to  the  trachea.  These 
cartilages,  which  are  called  vocal 
cords  can,  at  will,  be  made  tense 
or  loose,  and  also  can  separate  to 
a  greater  or  less  degree  so  as  to 
permit  more  or  less  air  to  pass 
either  way.  The  vibrations  of 
these  vocal  cords  when  air  is 
forced  through  the  orifice,  give 
rise  to  the  air  vibrations;  the 
degree  of  tension  given  to  them 
determines  the  pitch,  and  the 
amount  of  air  forced  through 
them  determines  the  loudness 

FIG.  162.  „  _,.  , 

01  the  sound. 

By  stretching  two  pieces  of  thin  rubber  membrane 
over  the  end  of  a  tube  so  as  to 
leave  a  narrow  fissure,  as  in  Fig. 
163,  an  artificial  glottis  can  be  made 
which,  if  blown  through,  will  pro-  FlG- 1C3- 

duce  a  sound,  the  pitch  of  which  will  depend  upon  how 
tightly  the  membrane  is  stretched. 

The  sound  waves  produced  by  the  cords  escape  by 
way  of  the  mouth  M  and  nose  cavity  C,  both  of  them 
acting  as  resonant  cavities.  The  mouth  can  be  greatly 
varied  in  size  by  the  movements  of  the  lower  jaw  L 
and  tongue  T,  soft  palate  U,  the  cheeks,  and  the  lips. 


SOUND.  295 

These  changes  in  size  greatly  modify  the  resonance. 
In  noting  the  movements  of  these  when  speaking  the 
vowels  a  e  i  o  w,  one  can  perceive  that  the  shape  of  the 
mouth  cavity  determines  what  sound  can  be  made. 
One  cannot  speak  the  letter  a  when  the  mouth  and 
tongue  are  in  proper  position  for  speaking  o.  The 
nasal  cavity  C  has  much  to  do  in  articulations,  and 
when  the  lining  membrane  is  swollen,  as  in  head  colds, 
or  the  nose  is  pinched  so  as  to  close  the  cavity,  many 
words  cannot  be  spoken  plainly,  especially  such  as 
require  the  sound  of  m  or  ng.  Pinch  the  nostrils  and 
try  to  say  the  word  "something,"  and  it  will  be  dis- 
covered how  important  the  resonating  cavity  of  the 
nose  is  for  articulation. 

In  different  individuals  the  size,  shape,  texture,  and 
muscular  control  of  each  of  these  differ  so  much  as  to 
give  character  to  the  sound  of  each  voice.  There  are 
not  less  than  a  hundred  different  muscles  called  into 
action  in  talking,  and  so  admirably  are  they  adjusted 
to  each  other  that  they  all  work  automatically  as  one 
complex  machine,  and  no  more  require  conscious  super- 
vision than  does  winking  or  walking. 

The  Opeidoscope.  —  The  string  telephone  indicates 
the  vibratory  motions  communicated  to  it  by  sound 
waves,  but  these  may  be  made  still  more  apparent  by 
tying  a  piece  of  letter-paper  over  one  end  of  a  tube  an 
inch  or  two  in  diameter  and  three  or  four  inches  long 
(Fig.  164),  and  gluing  a  bit  of  mirror  a  quarter  of  an 
inch  square  upon  the  middle  of  it.  If  light  be  directed 
upon  this  from  the  porte-lumiere  (p.  229),  and  the  beam 


296  NATURAL   PHILOSOPHY. 

be  reflected  to  the  wall,  ten  or  fifteen  feet  away,  in  a 
darkened  room,  any  vibratory  motion  of  the  paper  will 
be  indicated  by  the  movements  of  the  beam  of  light. 
If  sounds  be  made  in  the  open  end  of  the  tube,  various 
curves  will  be  described  on  the  wall,  and  by  tilting 
the  end  with  the  mirror,  complex  wave  figures  will  be 
formed,  which  will  depend  upon  the  pitch,  the  over- 
tones, and  the  loudness  of  the  sound.  If  a  tune  be 
_  ^  ^^^^^  tooted  into  it,  the  form  will 
^i  change  for  every  different  note, 
EJ  but  will  be  always  the  same  for 
^~~^_J  any  given  one.  This  instrument 

is  called  the  opeidoscope. 
FIG.  164. 

A  soap   film   stretched    across 

one  end  of  a  lamp  chimney  and  held  in  the  beam  from 
a  porte-lumiere  will  reflect  it  to  the  wall.  A  lens  with 
ten  or  twelve-inch  focus  will  give  an  enlarged  image  of 
the  film  upon  the  screen.  Prismatic  colors  may  be  seen, 
and  if  sounds  be  made  near  the  open  end  of  the  tube, 
the  film  will  be  colored  with  beautiful  coruscations, 
which  will  change  with  every  pitch  of  sound  made. 

The  Phonograph.  —  If  in  place  of  the  mirror  a  short 
needle  be  fixed  to  the  middle  of  the  vibrating  surface 
or  diaphragm,  as  at  b,  Fig.  165,  it  will  move  in  and  out 
as  often  as  the  diaphragm  does.  If  the  point  of  the 
needle  touches  a  surface  of  wax  spread  on  the  cylinder 
c  that  is  being  rotated,  a  series  of  indentations  will  be 
made  in  the  wax  corresponding  exactly  with  the  num- 
ber of  vibrations  that  the  needle  makes.  If  the  cylinder 
is  turned  round  so  as  to  permit  the  needle  to  fall  into 


SOUND.  297 

the  indentations  at  first  made,  its  rotation  will  cause 
the  needle,  and  with  it  the  diaphragm  to  which  it  is 
attached,  to  make  the  same  number  and  kind  of  vibra- 
tions that  produced  the  indentations.  It  will,  conse- 
quently, record  and 
reproduce  any  kind  of 
a  sound.  The  charac- 
teristics of  all  musical  ~ 
instruments  as  well  as  


of  voices,  may  be  pre-  Ro  165 

served  and  reproduced 

at  will.  This  machine  is  called  the  phonograph.  Its 
operation  is  an  illustration  of  what  was  said  on  page 
280,  that  sound  vibrations  cause  surfaces  upon  which 
they  fall  to  vibrate  in  like  manner  as  themselves.  It 
also  shows  that  in  speech  there  is  nothing  but  definite 
complex  vibratory  motion. 

Music.  —  When  a  single  sound  is  produced  by  the 
voice  or  upon  any  instrument,  as  a  flute  or  piano,  by 
striking  a  single  key,  that  sound  is  called  a  tone.  A 
number  of  tones  of  like  quality,  varying  more  or  less 
in  pitch,  following  each  other  with  regularity,  is  called 
;i  tune  or  melody.  Thus  the  notes  written  below  con- 


There's  no      place  like      home,      there's    no       place    like    home. 
Ki<;.  IOC. 

stitute  a  melody,  whether  played  upon  some  instrument 
or  hummed  by  the  voice. 


298  NATURAL   PHILOSOPHY. 

Whenever  words  are  sung  to  the  varying  notes  it  is 
called  a  somj.  Upon  many  musical  instruments  it  is 
impossible  to  produce  more  than  one  tone  at  a  time, 
for  example,  the  flute,  the  cornet;  also  with  the  voice. 
Other  instruments  permit  several  tones  to  be  made  upon 
them  at  the  same  time,  as  the  violin,  the  harp,  piano,  and 
organ.  It  is  a  fact  familiar  to  every  one  that  some 
sounds  when  heard  together  are  very  disagreeable  to 
the  ear,  yet  when  heard  separately  are  agreeable  enough, 
while  other  sounds  when  heard  together  are  pleasing. 

There  are  certain  relations  that  are  found  to  exist 
between  these  agreeable  and  disagreeable  sounds,  to 
understand  which  it  is  needful  to  be  acquainted  with 
the  musical  scale. 

It  is  customary  to  write  music  on  a  group  of  five 
lines,  called  the  staff.  Each  of  the  lines  and  spaces  is 
designated  by  a  letter  that  is  constant. 

The  staff  and  letters  are  thus  represented  (Fig.  167). 
Only  seven  letters  of  the  alphabet  are  used,  and  these 


are  repeated  above  and  below  as  far  as  necessary.  The 
musical  alphabet  begins  with  the  letter  C  in  the  place 
indicated  above,  and  if  notes  are  placed  upon  the  lines 
and  spaces  as  shown,  a  series  of  tones  will  be  repre- 
sented called  the  natural  scale,  which  is  sometimes  sung 
to  the  syllables  do,  re,  mi,  and  so  on.  If  the  note  C  be 
sung  or  played  at  the  same  time  as  the  note  D,  the 
result  is  a  higher,  unpleasant  sound,  which  is  called  a 


SOUND. 


299 


discord;  while  if  the  note  Gr  is  heard  with  the  note  <7, 
the  compound  sound  will  be  what  is  called  a  concord 
or  harmonious  sound.  In  like  manner,  the  sound  of 
the  higher  0  with  the  lower  C  is  tolerated  by  the  ear. 
These  sounds  all  differ  from  each  other  only  in  pitch. 

In  order  that  there  shall  be  uniformity  in  pitch, 
musicians  have  adopted  as 
a  standard  for  the  letter  C 
on  the  added  line  below 
the  staff  261  vibrations 
per  second.  This  C  is  the 
middle  C  of  the  piano. 

Let  the  sonometer  have 
both  strings  tuned  to  the 
same  pitch.  Calling  the 
tone  given  by  one  string  c7o, 
place  the  movable  bridge 
under  the  second  string 
near  one  end,  and  move  it 
sloAvly  towards  the  other 
end  until,  when  plucked, 

it  gives  the  tone  re  as  accurately  as  can  be  judged  by 
the  ear. 

Measure  the  length  of  both  strings.  The  shorter 
one  will  be  found  to  be  |  the  length  of  the  other.  Do 
the  same  for  each  letter,  and  make  a  table  of  the  meas- 
ures and  results  as  above. 

In  this  table  the  assumed  length  of  the  string  giving 
the  note  do  is  36  inches,  in  which  case  the  length  giving 
re  will  be  32  inches,  that  giving  *»l,  -\  inches,  and  so 
on  as  given.  The  ratio  of  32  to  36  is  as  8  to  9,  —  the 


NUMBER 

NAMB 

Ll=«°r 

RATIO 

I'M   ril.V] 

1 

1)0 

:;<; 

2 

Re 

32 

1 

3 

Mi 

28.8 

1 

4 

Fa 

27 

I 

5 

Sol 

24 

| 

6 

La 

21.6 

1 

7 

Si 

19.2 

A 

8 

Do 

18 

I 

300 


NATURAL   PHILOSOPHY. 


length  of  the  second  string  is  $•  the  length  of  the  first. 
The  ratio  of  24  to  36  is  as  2  to  3,  —  the  length  of  string 
for  sol  is  |  that  for  do;  and  so  on  for  each  of  the  others. 
As  the  vibratory  rates  of  strings  are  inversely  as  their 
lengths,  it  follows  that  the  vibratory  rate  of  re  is  -|  that 
of  do  ;  and  of  sol,  £  that  of  do.  The  fraction  represent- 
ing the  ratio  of  the  length  of  one  string  to  the  first  one 
will,  when  inverted,  represent 
their  relative  number  of  vibra- 
tions, or  while  do  makes  8  vibra- 
tions, re  makes  9,  and  while  do 
makes  2  vibrations,  sol  makes  3. 
If,  therefore,  the  fundamental 
do  be  tuned  to  standard  pitch  of 
256  vibrations,  re  will  make  256 
X  |  =  288,  and  sol  will  make 
256  X  |  =  384  in  a  second.  Com- 
puting the  values  of  each  of  the 
numters  of  the  scale  as  above, 
one  will  have  another  table  which 
will  represent  the  miml^er  of  vi- 
brations for  each  letter  of  the  scale. 
These  ratios  and  numbers  may  be  verified  in  another 
way.  Choose  two  glass  tubes  six  or  eight  inches  long 
and  half  an  inch  in  diameter.  Stop  one  end  of  one 
with  a  cork  and  blow  across  the  open  end  ;  it  will 
give  a  sound  of  definite  pitch.  Fit  a  cork  to  the  other 
tube,  such  as  will  fit  snugly  and  can  be  pushed  through 
it  at  will.  Adjust  this  cork  so  that  the  tube,  when 
blown  across,  will  give  the  same  pitch  as  the  first 
tube;  if  the  first  gives  do,  move  the  cork  in  the  second 


LETTER 

RATIO 

c 

256 

D 

I 

288 

E 

1 

320 

F 

f 

341^ 

G 

f 

384 

A 

f 

426] 

B 

¥ 

480 

C 

f 

512 

SOUND.  301 

tube  so  it  will  give  the  note  re ;  measure  the  lengths 
of  both  tubes  and  compare  them.  The  shorter  one  will 
be  found  to  be  f  the  length  of  the  longer.  In  like 
manner,  each  of  the  other  notes  of  the  scale  can  be 
sounded  by  shortening  to  the  proper  length  the  column 
of  air  in  the  tube  with  the  movable  plug;  the  ratios  of 
their  lengths  to  that  of  the  first  tube  will  give  the  same 
figures  as  those  given  by  the  sonometer. 

Such  a  series  of  fractions  as  those  given  above  are 
called  musical  ratios. 

Interference  of  Sound  Waves.  —  Strike  a  small 
tuning-fork,  and,  holding  it  near  the  ear,  roll  the  stem 
between  the  thumb  and  finger.  A  decided  change  in 
the  strength  of  the  sound  will  be  noticed,  and  if  the 
fork  be  carefully  tuned,  a  position  may  be  found  where 
the  sound  can  scarcely  be  heard,  and  a  slight  turn  from 
that  position  in  either  direction  will  make  the  sound 
again  audible.  This  may  be  understood  by  remembering 
that  the  two  prongs  of  the  fork  beat  towards  and  a\\  a  v 
from  each  other  while  vibrating,  hence  each  of  them 
will  be  generating  a  rarefaction  in  the  air  between  the 
prongs  at  the  same  time  they  are  condensing  the  air  in 
front  of  them.  But  the  rarefaction  can  be  conducted 
away  only  past  the  prongs,  then  it  begins  to  l>c  distrib- 
uted in  every  direction.  At  the  corners  the  rarefaction 
meets  the  condensation,  and  the  two  neutralize  each 
other  because  their  motions  are  in  opposite  directions. 
In  certain  directions  these  balance  each  other  so  there 
is  no  wave  motion  at  all,  and  consequently  no  sound. 
This  phenomenon  is  called  interference. 


302  NATURAL   PHILOSOPHY. 

When  two  sounds  are  nearly,  but  not  quite,  of  the 
same  pitch,  they  produce  what  are  called  beats,  which 
may  be  easily  heard  from  piano-strings  not  quite  in 
tune,  and  from  two  similar  tuning-forks,  if  one  has 
a  bit  of  wax  stuck  to  its  prongs.  If  one  sound  is  pro- 
duced by  256  vibrations  a  second,  and  the  other  by  257, 
the  combined  sound  will  be  stronger  once  a  second,  and 
the  beats  can  be  heard  without  difficulty;  if  they  differ 
by  two  or  three  vibrations  per  second,  there  will  be 
heard  two  or  three  beats  per  second.  The  greater  the 
difference,  the  more  frequent  the  beats,  and  presently 
the  beats  produced  in  this  way  quite  spoil  the  tones.  If, 
however,  the  beats  occur  as  many  as  twenty  or  more 
times  a  second,  they  give  a  continuous  sound  of  definite 
pitch.  If  the  number  of  beats  per  second  be  a  sub- 
multiple,  such  as  one-half  or  two-thirds  the  number  of 
vibrations  of  either  of  the  tones  that  produce  them, 
they  add  an  agreeable  constituent  to  the  sound,  and 
altogether  they  constitute  a  chord.  Thus  in  the  case 
of  the  two  notes  C  and  6r,  when  the  former  makes  256 
vibrations  and  the  latter  makes  384,  —  the  ratio  l>eing 
2  to  3,  —  the  number  of  beats  per  second  will  be  the 
difference  between  the  two  numbers,  namely,  1 28,  which 
is  one-half  of  256.  The  beats  coincide  with  the  funda- 
mental 128  times  a  second.  The  three  heard  together 
are  as  if  a  third  tone  an  octave  lower  had  been  added. 
When  C  and  D  are  sounded  together,  C  makes  256 
vibrations  and  D  288,  and  there  are  32  beats  per 
second.  The  compound  is  disagreeable  to  the  ear  and 
is  called  discordant. 

If  more  than  two  sounds  be  produced  together  they 


SOUND. 


303 


must  all  be  in  some  simple  ratio  to  each  other  if  they 
are  to  be  pleasing.  This  is  the  case  when  the  notes  of 
what  is  called  the  common  chord  are  sounded  together, 
in  which  we  have  the  ratio  CE,  f  :  CG-,  f  :  Ea,  f .  If 
more  notes  be  added  they  must  be  duplicates  of  these  in 
some  other  octave. 

Harmony.  —  When  music  is  thus  written  to  be 
played  or  sung  it  is  called  harmony,  and  throughout 
all  the  changes  of  pitch  in  each  part  the  simple  ratios 

AMERICA. 


My    conn  -  try,    'tis        of    thee, Sweet  Land    of       lib    -    er  -  ty. 


K    1    •  I     I      t  •  f     f '  1 


Of    thee     I     sing;     Land  where  my    fa  -  thers  died,  Land  of     the 

X  4          !i  I 

I  If 


pil-grim's  pride.From  ev  -  *ry  monn-tain's  side,   Let  free-dom  ring. 

*   i  *  *  *.!    *  i  >*!  *s   *     '• 

1       p      £1 — f(i  *      ^     y     M — 

^^  i*3 


304  NATURAL    PHILOSOPHY. 

given  are  maintained,  as  may  be  seen  by  taking  any 
four-part  music,  substituting  the  vibration  numbers  for 
the  notes,  putting  them  in  fractional  form,  and  reduc- 
ing them  to  their  lowest  terms. 

In  the  above  music,  written  in  two  parts,  treble  and 
bass,  the  ratios  as  expressed  by  the  fractions  are  written 
out  for  the  notes  sounded  together.  Observe  that  the 
numbers  are  all  such  as  have  been  described  as  derived 
from  the  measurement  of  vibration  numbers,  and  are 
essential  for  harmony.  The  ratio  2 : 3  occurs  eight  times, 
5 : 3  and  4 : 3  each  five  times,  and  5 : 4  six  times,  while 
such  as  16:9  occurs  but  twice,  and  64:45  only  once. 
If  other  parts  were  compared,  similar  ratios  would 
appear.  One  may  thus  verify  these  music  relations 
with  such  tunes  as  "  Auld  Lang  Syne "  or  "  Green- 
ville," when  arranged  in  two  or  more  party,  and  assure 
himself  that  part  music  and  all  harmony  consists  of 
sounds  whose  vibration  numbers  are  in  simple  ratios. 
and  that  any  departure  from  these  ratios  is  not  endured 
by  the  ear,  and  has  to  be  quickly  followed  by  notes 
with  the  required  relations. 

CHANGE  OF  KEY. 

Sharps  and  Flats.  —  The  natural  scale  which  we 
sing  or  play  (p.  298)  is  not  adapted  to  all  pieces  of 
music.  One  may  easily  satisfy  himself  on  this  point 
by  singing  "  America  "  on  the  pitch  of  C.  It  will  be 
found  too  low,  and  sonic  lii^hcr  pitch  must  be  chosen. 
When  a  different  pitch  is  taken  the  same  ratios  must 
be  kept,  and  we  do  keep  them  when  we  sing  do,  re,  mi 
of  the  scale. 


SOUND.  305 

On  the  staff  is  written  the  actual  vibration  numbers 
of  the  various  notes  opposite  the  notes  themselves.  If 
we  choose  the  pitch  of  Gr  for  the  new  scale,  calling  that 
note  do,  and  calculate  the  vibration  numbers  for  the 
new  scale,  they  all  will  be  found  to  agree  so  nearlv 
with  the  numbers  calculated  for  the  key  of  C  (except 
the  note  on  F  on  the  upper  line)  that  they  may  be 
used  for  musical  purposes.  The  note  on  F  for  the  key 
of  C  has  682  vibrations  (512  X  £),  while  for  the  key  of 
Gr  it  should  have  720  (384  X  -1/)-  This  number,  682, 
is  considerably  too  low  for  the  proper  pitch,  and  it 


*-*n 


II 


becomes  necessary  to  interpose  a  new  note  between  F 
and  Gr.  As  the  new  note  takes  the  place  of  F  and  is 
higher  in  pitch,  it  is  called  F  sharp,  and  is  marked  by 
the  symbol  $  to  indicate  it. 

If  the  pitch  of  F  is  chosen  for  the  new  scale  and  the 
vibration  numbers  for  C,  256,  be  compared  with  tin- 
numbers  computed  for  F,  341,  they  will  be  found  to 
coincide,  with  the  exception  of  one  on  the  letter  B. 
In  the  natural  scale  B  makes  256  X  Y'  =  48°  vibra- 
tions, but  the  fourth  in  the  scale  of  F  should  make 
341  X  ^  =  454  vibrations.  A  new  note  of  lower  pitch 
must  be  substituted  for  B  and  we  call  it  B  flat.  Thus 
by  using  any  one  of  the  vibration  nuinl>ers  of  the  natu- 
ral scale  of  C  as  a  basis,  and  multiplying  that  number 
liv  tlu>  scries  of  fractions  by  which  the  numbers  of  the 
scale  of  t"' wen-  obtained,  and  comparing  these  numbers 


306  NATURAL   PHILOSOPHY. 

with  those  of  the  scale  of  (7,  one  may  see  at  once  which 
letters  need  to  be  modified.  If  too  low,  a  sharp  (£)  is 
employed;  if  too  high,  a  flat  (b)  is  used.  Scales  built 
upon  other  tones  than  G  receive  the  name  of  the  tone 
they  are  built  upon,  as  the  key  of  G-  sharp,  the  key  of 
Bflat. 

Harmonic  Interference.  —  It  has  been  stated  that 
sounds  are  rarely  simple,  but  are  made  up  of  a  series 
of  sounds  which  are  multiples  of  the  lowest  or  funda- 
mental   sound.       If   we    have    different   fundamentals 
sounding  together,  then  overtones 
must  be  present  to  strengthen  or 
to  weaken  each  other  by  inter- 
ference.     Thus,   if   the   note   C 
(bass)   upon   a   piano  be   struck, 
the  overtones  belonging  to  it  are 
indicated  by  the  black  notes  upon 

the  staff.  E  and  G-  in  like  manner  have  their  over- 
tones represented.  If  the  C  and  E  be  compared,  the 
third  overtone  of  the  E  coincides  with  the  fourth 
of  the  (7,  and  the  first  and  third  of  the  G-  with  the 
second  and  fifth  of  C.  All  the  rest  are  more  or  less 
interfering  and  discordant.  If  it  were  not  for  the 
fact  that  the  higher  overtones  are  generally  feeble,  the 
most  of  that  which  we  now  call  music  would  be  unen- 
durable because  of  the  discordances  which  are  really 
present. 

Consider  what  a  number  of  sounds  there  must  be 
when  a  full  organ  is  played  with  the  harmony.  There 
may  be  as  many  as  fifty  or  more  si-rit's  of  pipes,  each 


SOUND.  307 

with  eight  or  more  pipes  sounding  at  one  time.  These 
would  give  us  many  as  i'mir  hundred  fundamental  sounds, 
while  the  overtones  must  be  reckoned  by  thousands. 
With  a  full  orchestra  with  twelve  or  fifteen  different 
kinds  of  instruments,  the  overtones  would  be  in  greater 
variety  than  on  the  organ.  The  vocal  organs  are  like 
a  musical  instrument,  and  the  overtones  are  not  alike 
in  pitch  or  intensity  for  any  two  individuals.  We 
therefore  hear  a  wonderful  variety  of  sounds  when  a 
hundred  or  more  persons  are  singing  together.  The 
interfering  sounds  and  high  overtones  do  not  have  suf- 
ficient intensity  to  be  heard  very  far,  hence  the  richness 
of  many  blended  voices  when  heard  at  the  distance  of 
two  or  three  hundred  feet  or  farther.  Such  sounds  as 
are  produced  by  many  persons  talking  at  once,  by  car- 
riages when  in  motion,  by  tin  horns  and  tin  pans,  all 
of  which  are  called  noises,  are  simply  compound  sounds 
without  definite  ratios  to  each  other,  and  hence  are 
discordant. 

The  Ear.  —  Thus  far  the  phenomena  of  sound  have 
been  considered  as  purely  physical,  the  origin  and  dis- 
tribution of  waves  in  the  air  and  in  other  elastic  bodies 
alone  being  regarded.  Such  phenomena  could  exi.-t 
and  be  studied  if  there  were  no  such  things  as  cars. 
just  as  the  physical  phenomena  of  the  ether  waves  could 
be  studied  without  eyes.  Eyes  and  ears  are  helpful 
in  either  study,  but  both  are  not  essential.  Physical 
phenomena  and  sensation  are  so  utterly  different  from 
each  other  that  they  cannot  be  compared.  A  needle- 
point  can  be  thrust  into  a  piece  of  wood  or  into  the 


308  -        NATURAL    PHILOSOPHY. 

finger,  the  physical  phenomena  are  the  same ;  but  in  the 
finger  there  is  a  sensation  of  pain  that  accompanies 
the  action,  but  is  not  a  part  of  it.  Sensation  implies 
a  nervous  system  and  a  sensorium,  that  is,  a  seat  of 
consciousness. 

Between  the  sound  vibrations  in  the  air  and  the  sen- 
sorium in  the  brain  there  is  a  complicated  piece  of  appar- 
atus called  the  ear.  In  man  the  external  part,  which  is 
called  the  pinna,  is  not  an  important  part  for  hearing, 
for  it  may  be  quite  removed  without  making  any  appre- 
ciable difference  in  the  per- 

'•(f)n5)      —*  ception    of    sounds.     The 

inner  part  is  a  series  of  tubes 
and  chambers  within  the 
solid  bony  structure  of  the 
skull.  A  small  tube  A, 
called  the  auditory  canal, 
opens  inward  to  the  depth 

.T.IAT.     J.JJ..  "11 

01    about    an    inch    and    a 

quarter.  The  inner  end  of  this  canal  is  closed  by  a 
membrane,  called  the  tympanic  membrane,  stretched 
across  it  at  an  angle.  It  is  curved  inward  at  its 
middle  part  as  if  pulled  from  within.  Behind  this 
membrane  is  an  air  chamber  B,  which  has  a  tube  C, 
called  the  eustachian  tube,  leading  to  the  back  of  the 
mouth.  In  this  chamber  are  three  small  bones:  one 
attached  to  the  middle  part  of  the  membrane,  the  second 
to  the  first,  and  the  third,  which  has  the  form  of  a 
stirrup,  is  made  fast  to  the  second  on  one  side  and  to 
another  membrane  on  the  side  opposite.  This  second 
membrane  closes  a  complicated  cavity,  the  bony  laby- 


SOUND.  309 

rinth  in  the  bone  of  the  skull.  This  labyrinth  is  filled 
with  fluid  in  which  floats  a  membranous  labyrinth  hav- 
ing several  distinct  parts.  On  one  side  of  the  sac  are 
three  *<' inicircular  canals  D,  and  on  the  other  a  coiled 
tube  E,  called  the  cochlea.  The  membranous  labyrinth 
in  turn  is  tilled  with  fluid  containing1  a  great  number  of 
minute  crystals  called  otoliths.  At  certain  places  inside 
the  sac,  canals,  and  cochlea,  are  small  bodies  known  as 
auditory  cells,  each  bearing  small  hairs  on  its  surface. 
The  structure  is  extremely  complicated  in  the  cochlea, 
where  there  is  an  apparatus  known  as  the  organ  of 
Corti,  made  up  of  over  three  thousand  sets  of  cells, 
each  set  consisting  of  five  or  more  cells.  The  audit"  UT 
nerve  G>  coming  from  the  brain  breaks  up  into  brandies 
going  to  each  group  of  cells  and  again  branching,  so 
that  every  cell  has  a  twig.  There  are  not  less  than 
20,000  of  these  fibres  of  Corti  in  each  human  ear. 

One  may-  now  trace  the  physical  actions  within  the 
ear.  The  air  vibrations  in  the  auditory  canal  make 
the  tympanic  membrane  vibrate;  this  in  turn  shakes 
the  series  of  bones,  and  the  stirrup  shakes  the  window 
membrane  to  the  labyrinth.  This  shakes  the  contained 
liquid,  otoliths,  fibres,  and  nerve  cells,  and  the  distnrln- 
anee  of  the  nerve  ends  is  transmitted  by  the  nerve  to 
the  seat  of  sensation.  Then  we  hear.  If  any  part  of 
this  mechanism  is  absent  or  impaired,  we  become  deaf. 
Thus,  if  the  tympanic  membrane  is  raptured  or  thick- 
ened so  it  cannot  vibrate,  deafness  is  the  result.  Sound 
vibrations  communicated  to  the  bones  of  the  head  may 
be  heard,  provided  the  interior  parts  «>!'  the  ear  are  in 
order.  A  tuning-fork  may  be  heard  by  touching  its 


310  NATURAL   PHILOSOPHY. 

stem  to  the  skull  or  teeth;  and  a  sheet  of  thin  wood 
or  metal  held  by  the  edge  between  the  teeth  enables 
some  persons  to  hear  better.  Such  a  device  is  called 
an  audiphone. 

From  the  auditory  canal  to  the  auditory  nerve  there 
is  simply  a  series  of  vibratory  movements,  which 
become  weaker  and  weaker  because  more  and  more 
diffused,  until  in  the  parts  of  the  labyrinth  they  can 
be  only  of  molecular  dimensions,  that  is,  only  mil- 
lionths  of  an  inch.  They  become  changed  in  magni- 
tude, not  in  character.  The  particular  functions  of 
these  various  parts  of  the  ear  are  but  partially  known. 
The  fibres  of  Corti  were  thought  for  a  time  to  be  sympa- 
thetic, so  that  each  one  could  respond  to  some  particular 
rate  of  vibration;  but  that  view  is  now  believed  to  be 
unfounded,  and  at  present  there  is  no  explanation  of 
what  goes  on  in  the  labyrinth.  Movements  of  some 
sort  are  traceable  to  the  base  of  the  brain;-  there  they 
are  interpreted  as  sounds.  How  physical  actions  of 
any  kind  can  produce  sensations  is  unimaginable. 

Limits  of  Audibility.  —  For  the  production  of  high 
musical  tones,  sets  of  steel  rods  are  used  that  have 
definite  lengths  and  diameters.  A  steel  rod  2.6  inches 
long  and  .78  of  an  inch  in  diameter  will  give  20,000 
vibrations  per  second.  As  the  rods  are  made  shorter 
the  pitch  becomes  higher,  so  that  one  1.8  inches  long 
gives  40,000  vibrations.  Most  persons  fail  to  hear  any 
sound  of  30,000  vibrations  per  second,  but  a  few  can 
hear  as  many  as  35,000  or  upwards.  It  is  altogether 
probable  that  this  limit  for  any  one  is  due  only  to  the 


SOUND.  311 

difficulty  there  is  in  giving  energy  enough  to  the  higher 
sounds,  rather  than  that  the  apparatus  for  hearing  is 
itself  limited.  One  is  not  called  deaf  because  he  can- 
not hear  a  weak  sound,  if  by  making  the  sound  stronger 
he  can  hear  it. 

All  sounds  involve  energy  in  the  mechanical  sense, 
so  that  all  problems  of  sound  are  problems  of  the  trans- 
ference and  transformation  of  energy. 


Electrical  Resistance,  Diameter,  Cross- Section,  etc.,  of 

Copper  Wire,  American  Gauge, 

Temperature  24°  C. 


Gauge 

No. 

SIZE. 

WEIGHT. 

RESISTANCE. 

Capacity 
in 
Amperes. 

Diam. 
in  In. 

Area  in 
Sq.  In. 

Lbs.  per 
1000  Ft. 

Feet  per 
Lb. 

Ohms  per 
1000  Ft. 

Feet  per 
Ohm. 

Ohms 
per  Lb. 

0000 

.4600 

.16G191 

639.60 

1.564 

0.051 

19929.7 

.0000785 

312 

000 

.4096 

.131790 

507.22 

1.971 

0.063 

15804.9 

.000125         262 

00 

.3648 

.104590 

402.25 

2.486 

0.080 

12534.2 

.000198 

220 

0 

.3249 

.082932 

319.17 

3.133 

0.101 

9945.3 

.000315 

185 

1 

.2893 

.065733 

252.98 

3.952 

0.127 

7882.8 

.000501 

156 

2 

.2576 

.052130 

200.63 

4.994 

0.160 

6251.4 

.000799 

131 

3 

.2294 

.041339 

159.09 

6.285 

0.202 

4957.3 

.001268 

110 

4 

.2043 

.032784 

126.17 

7.925 

0.254 

3931.6 

.002016 

92.3 

5 

.1819 

.025998 

100.05 

9.995 

0.321 

3117.8 

.003206 

77.6 

6 

.1620 

.020617 

79.34 

12.604 

0.404 

2472.4 

.005098 

65.2 

7 

.1443 

.016349 

62.92 

15.893 

0.509 

1960.6 

.008106 

54.8 

8 

.1285 

.012766 

49.90 

20.040 

0.643 

1555.0 

.01289 

46.1 

9 

.1144 

.010284 

39.58 

25.265 

0.811 

12333 

.02048 

38.7 

10 

.1014 

.008153 

31.38 

31.867 

1.023 

977.8 

.03259 

32.5 

12 

.0808 

.005129 

19.74 

50.659 

1.626 

615.02 

.08237 

23. 

14 

.0641 

.003147 

12.41 

80.580 

2.585 

386.80 

.20830 

16.2 

16 

.0508 

.002029 

7.81 

128.041 

4.582 

243.25 

.52638 

11.5 

18 

.0403 

.001276 

4.91 

203.666 

6.536 

152.99 

1.3312 

8.1 

20 

.0320 

.000802 

3.086 

324.045 

10.394 

96.21 

3.3438 

5.7 

25 

.0179 

.000252 

0.967 

1(04.126 

33.135 

30.18 

34.298 

2.4 

28 

.0126 

.000125 

0.484 

2066.116 

66.445 

15.05 

137.283 

1.4 

30 

.0100 

.000079 

0.302 

3311.258 

105.641 

9.466 

349.805 

1.0 

32 

.0079 

.000050 

0.190 

5263.158 

168.011 

5.952 

884.267 

0.70 

34 

.0063 

.000031 

0.121 

8264.463 

267.165 

3.743 

2207.98 

0.50 

36 

.0050 

.000020 

0.075 

13333.33 

424.65 

2.355 

5661.71 

0.35 

40 

.0031 

.000008 

0.030 

33333.33 

1074.11 

0.931 

35803.8 

0.17 

312 


Mechanical,  Heat,  and  Electrical  Equivalents. 


1  Foot-pound 


1  Horse-power  = 


.0000303  Horse-power  per  minute. 

.001818  "          "         "    second. 

.0003707  Watt  per  hour. 

.0226  "         "    minute. 

1.356  "         "    second. 

.001288  Heat  Unit. 

f  746  Watts. 

1.980000  Foot-pounds  per  hour. 

33000  "          "          "    minute. 

550  "         "          "    second. 

2550  Heat  Units  per  hour. 

42.53  "         "        "    minute. 

.707  "         "        "    second. 

778  Foot-pounds. 

.00039  Horse-power  per  hour. 

.0235  "          "         "    minute. 

1.41  "          "         "    second. 

0.29083  Watt  per  hour. 

17.45  "        "    minute. 

1046.98  "        "    second. 

2654.4  Foot-pounds  per  hour. 

44.239  "           "          "     minute. 

.737  "          "          "    second. 

.0013406  Horse-power. 

3.4384  Heat  Units  per  hour. 

.0573  "         "         "    minute. 

.000955  "         "        "    second. 


313 


INDEX. 


Absolute  Zero,  87. 
Acceleration,  35. 
Adhesion,  17. 
Air,  66. 
Pressure,  57. 

—  Pump,  58. 

Alternating  Currents,  161. 
Ammeter,  124. 

Arc  Light,  157. 
Armature,  163. 
Atmosphere,  56. 
Atoms,  4. 

Shape  of,  9. 

Attraction,  17. 

—  Gravitative,  19. 
Audibility,  Limits  of,  310. 
Barometer,  59. 
Batteries,"  125,  128. 

—  Action  in,  126. 

—  Energy  of,  130. 

—  Secondary,  179. 
Boiling  Point,  104. 
Bolometer,  245. 
Boyle's  Law,  60. 
Brightness,  212. 
Bunsen's  Cell,  128. 
Buoyancy,  61. 
Camera,  261. 

Cells,  Galvanic,  126. 
Charles'  Law,  87. 
Circuit,  Electric,  151. 


Circuit,  Magnetic,  140. 

—  Primary,  161. 

—  Secondary,  151. 
Cohesion,  17. 
Color  Sensation,  264. 
Commutator,  162. 
Conduction,  Heat,  8.8,  101. 

—  Electric,  134. 
Cooling,  101. 
Crystallization,  100. 
Current,  Alternating,  161. 

— -Induced,  151. 
Density,  14. 
Depolarizer,  129. 
Diffraction,  258. 
Dissociation,  97. 
Dynamo,  160,  164. 
Ear,  307. 
Earth,  Curvature,  37. 

—  Magnetism,  146. 
Echo,  286. 

Efficiency,  Steam-Engine,  109. 

—  Dynamo,  164. 
Elasticity,  16. 

Electric   Attraction  and    Repul- 
sion, 187. 
Electric  Current,  116. 

—  Energy,  123,  131,  153. 

—  Light,  157. 

—  Measurements,  125. 
Heating,  163. 


316 


INDEX. 


Electric  Pressure,  125. 

—  Units,  123. 

—  Field,  189. 
Machines,  192. 

—  Motor,  165. 
Electricity,  Origin  of,  114,  121. 

—  Static,  186. 

—  Nature  of,  200. 
Electro-Magnetism,  147. 

—  Chemical  Work,  175. 
Electroscope,  188. 
Elements,  3. 

—  Table  of,  5. 
Energy,  1,  43,  44. 

—  of  Coal,  110. 

—  Mechanical,  54. 

—  of  Bullet,  93. 

—  Radiant,  206. 

—  Rotary,  47. 
-  Vibratory,  46. 

—  Transformation  of,  101,  111. 

—  of  Battery,  131. 
Equilibrium,  43. 
Ether,  139. 


Pressure,  147. 

—  Waves,  204,  243. 
Velocity  of,  207. 

Evaporation,  81. 
Expansion,  Linear,  81. 

—  Cubic,  85. 

—  Gaseous,  86. 
Eye,  261. 

Falling  Bodies,  36. 
Field,  Magnetic,  140,  148. 

—  Electric,  189. 
Flotation,  60. 
Fluorescence,  186,  267. 
Foot-Pounds,  39,  43. 
Force,  39. 
Fraunhofer  Lines,  242. 


Free  Path,  13,  24,  67,  97. 
Fuels,  78. 
Fusion,  95,  96. 
Gas,  11. 

Pressure,  57. 

Gases,  Absorptive  Power  of,  241. 
Gaseous  Buoyancy,  61. 
Galvanic  Battery,  119. 
Galvanometer,  116. 
Gravity,  20,  35. 
Hardness,  17. 
Harmony,  303,  306. 
Heat,  68. 

—  Sources  of,  81. 

—  Origin  of,  61,  70,  71. 

—  Mechanical  Equivalent,  77. 

—  Units,  76,  79. 

—  Expansion,  81. 

—  Conduction,  88. 

—  Specific,  89. 

—  Phenomena  of,  81. 

Heating,  Electric,  153,  185. 

High  Electric-Pressure  Phenom- 
ena, 180. 

Incandescent  Light,  158. 
Induction  Coil,  181. 

—  Magnetic,  141,  149,  150. 
Inertia,  34. 

Key,  Change  of  Musical,  204. 
Latent  Heat,  105. 

—  Energy,  106. 
Lenses,  226,  230. 

—  Images  formed  by,  228. 
Lever,  49. 

Leyden  Jar,  194. 
Light  Ray,  210. 

—  Velocity  of,  139,  207, 
Lightning,  198. 

Liquid,  11. 

—  Pressure,  63. 
Machines,  49,  52. 


1NDKX. 


317 


Magnetic  Field,  140. 

—  Phantom,  137. 

—  Circuit,  140. 

—  Experiments;  141,  145. 

—  Induction,  141,  149,  150. 

—  Needle,  121,  115. 
Magnetism,  130. 

—  Electro,  147. 

—  of  the  Earth,  145. 

—  Effects  of  Heat  on,  14(5. 

—  Theory  of,  138,  144. 
Magnets,  136,  146. 
Mass,  19. 

Matter  Defined,  2. 

—  Kinds  of,  3. 

—  Divisibility  of,  4. 

—  States  of,  10. 
Mechanical  Equivalent,  77. 

—  Motion,  54. 
Melting,  95. 
Microscope,  231. 
Mirrors,  218. 
Molecules,  4. 

—  Size  of,  7,  8. 
Number  of,  8. 

—  Free  Path  of,  13. 
Motion,  23. 

Mechanical,  54. 

—  Molecular,  54. 

—  Translatory,  24. 

—  Transformations,  53. 

—  Hotary,  26. 

—  Vibratory,  25. 

—  Primary,  26. 

—  of  Machines.  i>0. 

—  Laws  of,  34,  185. 

—  Rates  of,  29,  30,  33. 
Music,  297. 

Nebula,  243. 
Nicnl's  Prism.  -J.V.. 
Odors,  11. 


Ohm's  Law,  123,  129. 
Opeidoscope,  295. 
Perpetual  Motion,  111. 
Phenomenon,  2. 
Phonograph,  296. 
Phosphorescence,  184,  -_'4<i,  -.'iKi. 
Photography,  24ii. 

—  Electric,  248. 
Photometer,  213. 
Physical  Action,  1. 

—  Science,  1. 
Pictures,  X-Kay,  249. 
Pitch,  271. 

Polarization  of  Batteries,  126. 

—  of  Light,  253. 
Porosity,  13. 
Power,  40,  51. 
Pressure,  39,  43,  51,  M. 

Influence  on  Fusion,  !><;. 

Prismatic  Refraction,  234. 
Projection,  229,  238. 
Pulley,  50. 

Pump,  Air,  58. 

Suction,  63. 

Radiation,  101. 

Radiometer,  250. 

Rates  of  Molecular  Vibration,  209, 

240. 

Reflection  of  Light,  215. 
Refraction  of  Light,  -J-_'.;.  •_'.;». 

—  Double,  251. 
Relay,  135,  168. 
Resistance.  Electric,  122,  135. 

—  Box,  125. 
Resonator,  283,  291. 
Rotation,  26,  32. 
Search  Light,  150. 
Second,  2'.i. 

Secondary  Batteries.  1711. 
Soap-Hubbies.  Thickness  of,  7. 
Solid.  11,  12. 


318 


INDEX. 


Solidification,  98. 
Sonometer,  287. 
Sound,  270. 

—  Vibrations,  Range  of,  272. 

—  Distribution  of,  273. 

—  Energy  of,  272. 

—  Analysis  of,  290. 
Speaking  Tubes,  279. 

—  Telephone,  170. 
Specific  Gravity,  64. 

—  Heat,  89,  92. 

—  Energy,  92. 
Spectrum  Analysis,  237,  245. 
State,  Changes  of,  94. 
States  of  Matter,  10,  94. 
Steam-Engine,  107. 

—  Efficiency,  109. 

—  Energy  of,  106. 

—  Working  Power  of,  107. 
Storage,  Electrical,  194. 
String  Telephone,  279. 
Suction-Pump,  63. 
Surface  Tension,  103. 
Sympathetic  Vibratipns,  281. 
Table  of  Elements,  5. 

—  of  Electrical  Resistance,  312. 

—  of    Mechanical    and     Heat 
Units,  313. 

Telegraph,  166. 

—  Chemical,  168. 
Telegraphing  without  Wires,  173. 

—  by  Induction,  174. 
Telephone,  170,  172. 


Telescope,  233. 
Temperature,  12,  72. 
Tension,  Surface,  103. 
Thermodynamics,  76. 
Thermometer,  73. 
Thermopile,  118. 
Time,  Standard  of,  29. 
Transformations  of  Energy,  101. 
Transmitters,  Mechanical,  169. 
Tubes,  Geissler's  and  Crookes', 

182. 

Tuning-Fork,  25. 
Vacuum,  58. 
Velocity  of  Sound,  277. 

—  of  Light,  207. 

—  of  Wind,  56. 
Vibration,  25,  31,  208,  288. 
Sympathetic,  281. 

—  Sound,  283. 
Vision,  263. 
Voice,  293. 
Voltmeters,  124. 
Vortex  Rings,  9. 
Wave-Lengths,  208. 
Waves,  Ether,  204.   - 

—  Sound,  274. 

—  Invisible,  244. 
Work,  39. 

—  Rate  of,  44. 
X-Rays,  249. 
Zero,  Absolute,  87. 

—  Fahrenheit,  74. 
Centigrade,  74. 


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